Multiple Correct Answers MCQs for Sub-Topics of Topic 3: Quantitative Aptitude

Question 1. Which of the following statements are correct regarding the ratio of two quantities?

(A) The two quantities must be of the same unit.

(B) The ratio has no unit.

(C) The order of terms in a ratio is important.

(D) A ratio is always expressed as a fraction in its simplest form.

(E) The first term of the ratio is called the consequent and the second term is called the antecedent.

Question 2. Identify the proportions from the following:

(A) $2 : 3 :: 4 : 6$

(B) $5 : 10 :: 1 : 2$

(C) $3 : 4 :: 6 : 9$

(D) $10 : 15 :: 20 : 30$

(E) $1 : 2 :: 3 : 4$

Question 3. If $\frac{a}{3} = \frac{b}{4} = \frac{c}{5}$, which of the following ratios are equal to $a:b:c$?

(A) $6 : 8 : 10$

(B) $3 : 4 : 5$

(C) $9 : 12 : 15$

(D) $1/3 : 1/4 : 1/5$

(E) $1 : 2 : 3$

Question 4. If the cost of 5 kg of rice is $\textsf{₹}250$, which of the following can be determined using the unitary method?

(A) The cost of 1 kg of rice.

(B) The cost of 12 kg of rice.

(C) The quantity of rice that can be bought for $\textsf{₹}1000$.

(D) The time taken to cook 1 kg of rice.

(E) The number of grains in 1 kg of rice.

Question 5. A mixture contains milk and water in the ratio 3 : 2. If 10 litres of this mixture is removed and replaced with 10 litres of milk, which of the following statements could be true about the new mixture?

(A) The amount of milk increases.

(B) The amount of water decreases.

(C) The total quantity of the mixture remains the same.

(D) The ratio of milk to water increases.

(E) The ratio of milk to water decreases.

Question 6. Consider the proportion $a : b :: c : d$. Which of the following statements are true?

(A) $a \times d = b \times c$

(B) $\frac{a}{b} = \frac{c}{d}$

(C) $a, b, c, d$ are in continued proportion.

(D) $a, d$ are called extreme terms and $b, c$ are called mean terms.

(E) $a : c :: b : d$ (alternendo property)

Question 7. If $\frac{P}{Q} = \frac{R}{S}$, which of the following are valid transformations of this proportion?

(A) $\frac{Q}{P} = \frac{S}{R}$ (Invertendo)

(B) $\frac{P+Q}{Q} = \frac{R+S}{S}$ (Componendo)

(C) $\frac{P-Q}{Q} = \frac{R-S}{S}$ (Dividendo)

(D) $\frac{P+Q}{P-Q} = \frac{R+S}{R-S}$ (Componendo & Dividendo)

(E) $P \times R = Q \times S$

Question 8. The ratio of speeds of two cars is 4 : 5. If the first car covers a certain distance in 10 hours, which of the following statements are true about the second car covering the *same* distance?

(A) The second car is faster than the first car.

(B) The second car will take less than 10 hours.

(C) The time taken by the second car is proportional to its speed.

(D) The ratio of times taken is 5 : 4.

(E) The second car takes 8 hours.

Question 9. $\textsf{₹}720$ is divided among A, B, and C in the ratio $1/2 : 1/3 : 1/4$. Which of the following are correct shares?

(A) A gets $\textsf{₹}360$.

(B) B gets $\textsf{₹}240$.

(C) C gets $\textsf{₹}180$.

(D) The ratio of their shares is 6 : 4 : 3.

(E) The total share of A and B is $\textsf{₹}600$.

Question 10. If 12 men can do a piece of work in 24 days, and 18 women can do the same work in 16 days, which of the following statements are true?

(A) Work done by 1 man in 1 day is equal to work done by 1 woman in 1 day.

(B) Work done by 1 man in 1 day is more than work done by 1 woman in 1 day.

(C) The ratio of efficiency of a man to a woman is 2 : 3.

(D) 6 men can complete the work in 48 days.

(E) 9 women can complete the work in 32 days.

Question 11. The ratio of the number of students in three classes is 2 : 3 : 4. If 12 students are added to each class, the ratio becomes 8 : 11 : 14. Which of the following are true about the original number of students in the classes?

(A) The original number of students in the first class was 24.

(B) The original number of students in the second class was 36.

(C) The original number of students in the third class was 48.

(D) The total original number of students was 108.

(E) The difference between the number of students in the third and first class originally was 24.

Question 12. If $A : B = 3 : 4$ and $C : D = 5 : 6$, and $A=C$, then which of the following are true?

(A) $B : D = 4 : 6$

(B) $B : D = 2 : 3$

(C) $A : B : C : D$ cannot be uniquely determined.

(D) If $A=15$, then $B=20$ and $C=15$.

(E) If $A=15$, then $D=18$.

Question 1. If $y$ varies directly as $x$, i.e., $y \propto x$, which of the following statements are true?

(A) The graph of $y$ vs $x$ is a straight line passing through the origin.

(B) $\frac{y}{x}$ is a constant.

(C) When $x$ increases, $y$ decreases.

(D) $y = kx$ for some constant $k$.

(E) $y_1 x_2 = y_2 x_1$ for any two pairs $(x_1, y_1)$ and $(x_2, y_2)$.

Question 2. If $y$ varies inversely as $x$, i.e., $y \propto \frac{1}{x}$, which of the following statements are true?

(A) The graph of $y$ vs $x$ is a straight line.

(B) $y \times x$ is a constant.

(C) When $x$ increases, $y$ decreases.

(D) $y = \frac{k}{x}$ for some constant $k$.

(E) $y_1 x_1 = y_2 x_2$ for any two pairs $(x_1, y_1)$ and $(x_2, y_2)$.

Question 3. The cost of fencing a circular field is directly proportional to its radius. The area of the field is directly proportional to the square of its radius. Which of the following statements are correct?

(A) Cost of fencing varies directly as the diameter.

(B) Area varies directly as the square of the diameter.

(C) Cost of fencing is inversely proportional to the area.

(D) Area is directly proportional to the square of the cost of fencing.

(E) If the radius is doubled, the area becomes four times.

Question 4. If $A \propto B$ and $B \propto C$, which of the following are necessarily true?

(A) $A \propto C$

(B) $A \propto \frac{1}{C}$

(C) $A \propto B^2$

(D) $A = k_1 B$ and $B = k_2 C$ for some constants $k_1, k_2$.

(E) $A = K C$ for some constant $K$.

Question 5. The speed of a moving object is inversely proportional to the time taken to cover a fixed distance. If the speed is $v$ and time is $t$, which relations hold true for two different instances $(v_1, t_1)$ and $(v_2, t_2)$?

(A) $\frac{v_1}{t_1} = \frac{v_2}{t_2}$

(B) $v_1 t_1 = v_2 t_2$

(C) $v_1 t_2 = v_2 t_1$

(D) $\frac{v_1}{v_2} = \frac{t_2}{t_1}$

(E) $v \times t = \text{constant}$

Question 6. If $P$ varies directly as $Q$ and inversely as the square of $R$, which of the following relationships could represent this variation?

(A) $P = k \frac{Q}{R^2}$ for some constant $k$.

(B) $P R^2 \propto Q$

(C) $\frac{P R^2}{Q}$ is a constant.

(D) $P Q R^2 = \text{constant}$

(E) If $Q$ is doubled and $R$ is halved, $P$ becomes 8 times its original value.

Question 7. If the number of articles purchased is $n$ and the cost per article is $c$, and the total cost is $T$, where $T = n \times c$. Which of the following are true statements about variation?

(A) If $c$ is constant, $T$ varies directly as $n$.

(B) If $n$ is constant, $T$ varies directly as $c$.

(C) If $T$ is constant, $n$ varies inversely as $c$.

(D) If $n$ is doubled and $c$ is halved, $T$ remains the same.

(E) $n$ varies inversely as $T$ if $c$ is constant.

Question 8. Given that $y$ is directly proportional to $x$ and $y=12$ when $x=3$. Which of the following are correct?

(A) The constant of variation is 4.

(B) The equation relating $y$ and $x$ is $y=4x$.

(C) When $x=5$, $y=20$.

(D) When $y=36$, $x=9$.

(E) The graph of $y$ vs $x$ passes through $(1, 4)$.

Question 9. Given that $a$ is inversely proportional to $b$ and $a=10$ when $b=2$. Which of the following are correct?

(A) The constant of variation is 20.

(B) The equation relating $a$ and $b$ is $a = \frac{20}{b}$.

(C) When $b=5$, $a=4$.

(D) When $a=2.5$, $b=8$.

(E) The graph of $a$ vs $b$ is a straight line.

Question 10. If the work done ($W$) is directly proportional to the number of workers ($N$) and the time taken ($T$), which of the following can be inferred?

(A) $W \propto N \times T$

(B) $W = kNT$ for some constant $k$ (efficiency per worker).

(C) If the number of workers is doubled and the time is halved, the work done remains the same.

(D) If the work done is fixed, the number of workers is inversely proportional to the time taken.

(E) If the number of workers is fixed, the work done is directly proportional to the time taken.

Question 11. If the volume of a sphere ($V$) varies directly as the cube of its radius ($r$), which of the following statements are true?

(A) $V = kr^3$ for some constant $k$.

(B) If the radius is doubled, the volume becomes 6 times.

(C) If the radius is halved, the volume becomes one-eighth.

(D) $\frac{V}{r^3}$ is a constant for any sphere.

(E) The constant $k$ is $\frac{4}{3}\pi$.

Question 12. If the pressure ($P$) of a gas varies inversely as its volume ($V$) at a constant temperature (Boyle's Law), which of the following statements are correct?

(A) $PV = \text{constant}$.

(B) $P_1 V_1 = P_2 V_2$ for any two states $(P_1, V_1)$ and $(P_2, V_2)$.

(C) As pressure increases, volume decreases.

(D) As pressure decreases, volume increases.

(E) The graph of $P$ vs $V$ is a straight line.

Question 1. Which of the following are equivalent to 50%?

(A) 0.5

(B) $1/2$

(C) 50/100

(D) Ratio 1 : 2

(E) 500 per mille

Question 2. A quantity is increased by 20%. Which of the following multipliers represent this increase?

(A) 1.20

(B) $120/100$

(C) $6/5$

(D) $1 + 0.20$

(E) $1 - 0.20$

Question 3. A quantity is decreased by 10%. Which of the following multipliers represent this decrease?

(A) 0.90

(B) $90/100$

(C) $9/10$

(D) $1 + 0.10$

(E) $1 - 0.10$

Question 4. If 30% of a number is 90, which of the following statements are true?

(A) The number is 300.

(B) 10% of the number is 30.

(C) 50% of the number is 150.

(D) The number can be found by calculating $\frac{90}{30} \times 100$.

(E) The number can be found by calculating $90 \times 0.30$.

Question 5. The price of an article increased by 25%. Which of the following statements are true?

(A) The new price is 125% of the original price.

(B) The new price is 1.25 times the original price.

(C) If the original price was $\textsf{₹}100$, the new price is $\textsf{₹}125$.

(D) To get back to the original price from the new price, the new price must be decreased by 20%.

(E) The increase in price is 1/4 of the original price.

Question 6. In an exam, 40% of students failed. Which of the following statements are true?

(A) 60% of students passed.

(B) The ratio of failed to passed students is 2 : 3.

(C) If the total number of students was 200, 80 students failed.

(D) If 120 students passed, the total number of students was 200.

(E) The percentage of students who passed is 100% - 40%.

Question 7. A salary is first increased by 10% and then decreased by 10%. Which of the following statements are true?

(A) There is no overall change in salary.

(B) The overall change is a decrease of 1%.

(C) If the original salary was $\textsf{₹}10000$, the new salary is $\textsf{₹}9900$.

(D) The final salary is 99% of the original salary.

(E) This is an example of successive percentage change.

Question 8. A student scores 75% marks in an exam. Which of the following can be the possible marks obtained and the total marks?

(A) Marks obtained = 75, Total marks = 100

(B) Marks obtained = 150, Total marks = 200

(C) Marks obtained = 300, Total marks = 400

(D) Marks obtained = 60, Total marks = 80

(E) Marks obtained = 50, Total marks = 75

Question 9. If A's income is 20% less than B's income, which of the following statements are true?

(A) A's income is 80% of B's income.

(B) A's income is 0.8 times B's income.

(C) If B's income is $\textsf{₹}10000$, A's income is $\textsf{₹}8000$.

(D) B's income is 25% more than A's income.

(E) The ratio of A's income to B's income is 4 : 5.

Question 10. The value of a property increases by 10% in the first year and by 20% in the second year. Which of the following statements are true about the total percentage increase over two years?

(A) The total increase is 30%.

(B) The total increase is 32%.

(C) The final value is 1.32 times the original value.

(D) The final value is $(1 + 0.10) \times (1 + 0.20)$ times the original value.

(E) This is an example of simple percentage increase.

Question 11. In a town, 60% of the population are men and 40% are women. 20% of the men are literate and 30% of the women are literate. Which of the following statements are true?

(A) 12% of the total population are literate men.

(B) 12% of the total population are literate women.

(C) The total percentage of literate people in the town is 24%.

(D) The percentage of illiterate men is 48% of the total population.

(E) The percentage of illiterate women is 28% of the total population.

Question 12. Which of the following fractions are equivalent to 75%?

(A) $3/4$

(B) $6/8$

(C) $15/20$

(D) $75/100$

(E) $5/6$

Question 1. If the Selling Price (SP) of an article is greater than its Cost Price (CP), which of the following statements are true?

(A) There is a profit.

(B) Profit = SP - CP.

(C) Profit percentage = $\frac{\text{Profit}}{\text{CP}} \times 100$.

(D) The transaction results in a loss.

(E) SP = CP + Profit.

Question 2. If the Cost Price (CP) of an article is greater than its Selling Price (SP), which of the following statements are true?

(A) There is a loss.

(B) Loss = CP - SP.

(C) Loss percentage = $\frac{\text{Loss}}{\text{CP}} \times 100$.

(D) The transaction results in a profit.

(E) CP = SP + Loss.

Question 3. The marked price of an article is $\textsf{₹}500$. A discount of 10% is offered on it. Which of the following statements are true?

(A) The discount amount is $\textsf{₹}50$.

(B) The Selling Price (SP) is $\textsf{₹}450$.

(C) The SP is 90% of the marked price.

(D) Discount is calculated on the Cost Price.

(E) SP = Marked Price - Discount.

Question 4. A shopkeeper sells an article at a profit of 20%. Which of the following statements are true?

(A) SP = 1.20 $\times$ CP.

(B) SP is 120% of CP.

(C) If CP = $\textsf{₹}100$, SP = $\textsf{₹}120$.

(D) Profit percentage is calculated on SP.

(E) Profit = 0.20 $\times$ CP.

Question 5. An article is sold at a loss of 15%. Which of the following statements are true?

(A) SP = 0.85 $\times$ CP.

(B) SP is 85% of CP.

(C) If CP = $\textsf{₹}200$, SP = $\textsf{₹}170$.

(D) Loss = 0.15 $\times$ CP.

(E) SP = CP - Loss.

Question 6. A dishonest shopkeeper sells goods at cost price but uses a faulty weight. If he uses a weight of 950 grams for 1 kg, which of the following statements are true about his transaction?

(A) He is making a profit.

(B) His gain is 50 grams for every 950 grams sold.

(C) His gain percentage is $\frac{50}{950} \times 100$.

(D) His gain percentage is $\frac{50}{1000} \times 100$.

(E) His gain percentage is approximately 5.26%.

Question 7. A shopkeeper marks up the price of an article by 30% and then gives a discount of 20%. Which of the following statements are true about his net profit or loss?

(A) His net gain is 10%.

(B) His net gain is 4%.

(C) The final selling price is $1.30 \times 0.80$ times the cost price.

(D) The final selling price is $1.04$ times the cost price.

(E) If the cost price is $\textsf{₹}100$, the marked price is $\textsf{₹}130$ and the selling price is $\textsf{₹}104$.

Question 8. The Cost Price of 12 articles is equal to the Selling Price of 10 articles. Which of the following statements are true?

(A) CP < SP for one article.

(B) There is a profit in the transaction.

(C) Profit is earned on the Cost Price.

(D) Profit percentage is $\frac{12-10}{10} \times 100$.

(E) The profit percentage is 20%.

Question 9. A shopkeeper sells two items at $\textsf{₹}1000$ each. He gains 10% on one and loses 10% on the other. Which of the following statements are true?

(A) His net result is no profit, no loss.

(B) He incurs a net loss.

(C) The percentage loss is given by $(\text{common gain or loss}\%)^2 / 100$.

(D) His net loss percentage is 1%.

(E) The total selling price is $\textsf{₹}2000$.

Question 10. A single discount equivalent to successive discounts of 20% and 10% is:

(A) 28%

(B) Calculated as $(100 - 20)\% \text{ of } (100 - 10)\%$ subtracted from 100%.

(C) Calculated as $20 + 10 - \frac{20 \times 10}{100} \%$.

(D) Equivalent to a single discount of 30%.

(E) Less than the sum of individual discounts.

Question 11. An article is sold at a profit of $\textsf{₹}50$. Which of the following is possible?

(A) CP = $\textsf{₹}200$, Profit % = 25%

(B) CP = $\textsf{₹}250$, SP = $\textsf{₹}300$

(C) CP = $\textsf{₹}500$, Profit % = 10%

(D) SP = $\textsf{₹}300$, CP = $\textsf{₹}250$

(E) SP = $\textsf{₹}550$, Loss = $\textsf{₹}50$

Question 12. The ratio of CP and SP of an article is 5 : 6. Which of the following are true?

(A) Profit percentage is 20%.

(B) Profit is $1/5$ of CP.

(C) Profit is $1/6$ of SP.

(D) If CP = $\textsf{₹}500$, SP = $\textsf{₹}600$ and profit is $\textsf{₹}100$.

(E) If profit is $\textsf{₹}20$, CP = $\textsf{₹}100$ and SP = $\textsf{₹}120$.

Question 13. Which of the following relationships correctly connect Cost Price (CP), Selling Price (SP), Marked Price (MP), Discount (D), Profit (P), and Loss (L)?

(A) SP = MP - D

(B) SP = CP + P

(C) SP = CP - L

(D) MP = CP + Markup

(E) Profit % = $\frac{SP - CP}{CP} \times 100$

Question 1. For Simple Interest (SI), which of the following statements are true?

(A) The interest is calculated only on the principal amount.

(B) The interest amount remains constant for each time period.

(C) Amount = Principal + SI.

(D) $\text{SI} = \frac{P \times R \times T}{100}$, where P is principal, R is rate, T is time.

(E) The amount grows exponentially over time.

Question 2. For Compound Interest (CI), which of the following statements are true?

(A) Interest is calculated on the principal plus accumulated interest.

(B) The interest amount increases with each compounding period.

(C) Amount = $P \left(1 + \frac{R}{100}\right)^T$, where P is principal, R is rate per period, T is number of periods.

(D) CI = Amount - Principal.

(E) The amount grows linearly over time.

Question 3. A sum of $\textsf{₹}10000$ is invested at 10% per annum. Which of the following are correct calculations?

(A) SI for 1 year = $\textsf{₹}1000$.

(B) CI for 1 year (compounded annually) = $\textsf{₹}1000$.

(C) SI for 2 years = $\textsf{₹}2000$.

(D) CI for 2 years (compounded annually) = $\textsf{₹}2100$.

(E) The difference between CI and SI for 2 years is $\textsf{₹}100$.

Question 4. When interest is compounded half-yearly, which of the following adjustments are made to the annual rate (R) and time period (T)?

(A) The rate used is R/2.

(B) The rate used is R/4.

(C) The number of periods is 2T.

(D) The number of periods is 4T.

(E) The formula for amount becomes $P \left(1 + \frac{R/2}{100}\right)^{2T}$.

Question 5. A sum of money doubles itself at Simple Interest in 5 years. Which of the following statements are true?

(A) The rate of interest is 20% per annum.

(B) The rate of interest is 10% per annum.

(C) In 10 years, the sum will become 4 times itself.

(D) In 15 years, the sum will become 8 times itself.

(E) In 2.5 years, the sum will become 1.5 times itself.

Question 6. A sum of money doubles itself at Compound Interest in 5 years. Which of the following statements are true?

(A) In 10 years, the sum will become 3 times itself.

(B) In 10 years, the sum will become 4 times itself.

(C) In 15 years, the sum will become 8 times itself.

(D) If the sum becomes $2^n$ times, the time taken is $n \times 5$ years.

(E) The rate of interest cannot be determined without more information.

Question 7. The value of a machine depreciates at a constant rate. Which of the following applies to this situation?

(A) It is similar to simple interest calculation.

(B) It is similar to compound interest calculation (with a negative rate).

(C) The value after T years = $P \left(1 - \frac{R}{100}\right)^T$, where P is original value, R is depreciation rate.

(D) The value decreases by the same amount each year.

(E) The rate of decrease in value slows down over time (in terms of absolute amount).

Question 8. The difference between CI and SI for 2 years on a sum P at R% per annum is given by $\frac{PR^2}{100^2}$. Which of the following statements are true?

(A) This formula is valid for compounding annually.

(B) This formula is valid for any compounding period.

(C) If R = 10% and difference is $\textsf{₹}10$, then P = $\textsf{₹}1000$.

(D) The difference increases as the principal increases.

(E) The difference increases as the rate increases.

Question 9. A sum of money is invested at a certain rate of SI. It amounts to $\textsf{₹}A_1$ in $T_1$ years and $\textsf{₹}A_2$ in $T_2$ years ($T_2 > T_1$). Which of the following are true?

(A) The interest for $(T_2 - T_1)$ years is $A_2 - A_1$.

(B) The interest for 1 year is $\frac{A_2 - A_1}{T_2 - T_1}$.

(C) The principal $P = A_1 - (\text{Interest for } T_1 \text{ years})$.

(D) The rate of interest can be calculated.

(E) This method only works for compound interest.

Question 10. If the nominal rate of interest is 8% per annum, which of the following are true about the effective annual rate?

(A) If compounded annually, the effective rate is 8%.

(B) If compounded half-yearly, the effective rate is greater than 8%.

(C) If compounded quarterly, the effective rate is greater than the rate compounded half-yearly.

(D) If compounded monthly, the effective rate is less than the rate compounded quarterly.

(E) The more frequent the compounding, the higher the effective rate.

Question 11. A loan is taken at a fixed interest rate. Which of the following factors influence the total amount of interest paid?

(A) The principal amount.

(B) The rate of interest.

(C) The time period of the loan.

(D) Whether the interest is simple or compound.

(E) The frequency of compounding (for compound interest).

Question 12. The CI on a sum for 2 years at 5% per annum is $\textsf{₹}328$. Which of the following are true?

(A) The SI on the same sum for the same period and rate is less than $\textsf{₹}328$.

(B) The SI on the same sum for the same period and rate is $\textsf{₹}320$.

(C) The principal sum is $\textsf{₹}3200$.

(D) The difference between CI and SI is $\textsf{₹}8$.

(E) The amount after 2 years is $\textsf{₹}3528$.

Question 1. Which of the following are subsumed under Goods and Services Tax (GST) in India?

(A) Central Excise Duty

(B) Service Tax

(C) Value Added Tax (VAT)

(D) Customs Duty

(E) Income Tax

Question 2. In an intra-state supply of goods or services, which components of GST are typically applicable?

(A) CGST

(B) SGST

(C) IGST

(D) UTGST (if applicable)

(E) Cess

Question 3. In an inter-state supply of goods or services, which component of GST is typically applicable?

(A) CGST

(B) SGST

(C) IGST

(D) UTGST

(E) Customs Duty

Question 4. If the price of an article before GST is $\textsf{₹}1000$ and the GST rate is 18%, which of the following statements are true?

(A) The amount of GST is $\textsf{₹}180$.

(B) The final price including GST is $\textsf{₹}1180$.

(C) The final price is 118% of the original price.

(D) If this is an intra-state sale, CGST = $\textsf{₹}90$ and SGST = $\textsf{₹}90$.

(E) If this is an inter-state sale, IGST = $\textsf{₹}180$.

Question 5. A product is sold for $\textsf{₹}2950$ including 18% GST. Which of the following statements are true?

(A) The price before GST is $\frac{2950}{1.18}$.

(B) The price before GST is $\textsf{₹}2500$.

(C) The amount of GST is $\textsf{₹}450$.

(D) If the seller made a profit of 20% on the price before GST, the Cost Price before GST was $\textsf{₹}2083.33$ (approx).

(E) The GST amount is 18% of $\textsf{₹}2950$.

Question 6. Input Tax Credit (ITC) under GST allows businesses to reduce their tax liability by which of the following means?

(A) By claiming credit for taxes paid on input goods or services.

(B) By reducing the tax payable on output supply.

(C) It helps in avoiding the cascading effect of taxes.

(D) It is available only to registered businesses.

(E) It applies to taxes paid on personal consumption.

Question 7. Which of the following are benefits of implementing GST?

(A) Simplification of indirect tax structure.

(B) Reduction in the multiplicity of taxes.

(C) Creation of a common national market.

(D) Boosting exports.

(E) Elimination of cascading of taxes.

Question 8. An article is marked at $\textsf{₹}500$. A discount of 20% is offered. GST is applicable at 12% on the discounted price. Which of the following are true?

(A) The discount amount is $\textsf{₹}100$.

(B) The price after discount is $\textsf{₹}400$.

(C) The amount of GST is $\textsf{₹}48$.

(D) The final selling price is $\textsf{₹}448$.

(E) The GST is calculated on the marked price.

Question 9. A manufacturer sells goods to a wholesaler for $\textsf{₹}10000$ (exclusive of GST). The wholesaler adds a margin of $\textsf{₹}2000$ and sells to a retailer (exclusive of GST). The GST rate is 18%. Assuming intra-state sales and full ITC, which of the following are true about the GST collected and paid?

(A) Manufacturer charges $\textsf{₹}1800$ GST from the wholesaler.

(B) Wholesaler's selling price is $\textsf{₹}12000$ (exclusive of GST).

(C) Wholesaler charges $\textsf{₹}2160$ GST from the retailer.

(D) Wholesaler pays net GST of $\textsf{₹}360$ to the government.

(E) Wholesaler pays total GST of $\textsf{₹}2160$ to the government.

Question 10. Which of the following are key features of GST?

(A) Destination-based consumption tax.

(B) Tax is levied at multiple points from manufacturing to consumption.

(C) Input Tax Credit mechanism.

(D) Uniform tax rates across the country for the same goods/services.

(E) It simplifies compliance for businesses.

Question 11. A price tag shows $\textsf{₹}590$ including 18% GST. Which of the following calculations are correct to find the price before GST?

(A) $\frac{590}{118} \times 100$

(B) $590 \times \frac{100}{118}$

(C) $\frac{590}{1.18}$

(D) $590 - 18\%$ of $590$

(E) $590 - \frac{18}{118} \times 590$

Question 12. Which of the following are examples of taxes that were NOT subsumed by GST?

(A) Stamp Duty

(B) Professional Tax

(C) Basic Customs Duty

(D) State VAT

(E) Central Sales Tax

Question 1. A can do a piece of work in $x$ days. Which of the following statements are true?

(A) In one day, A does $\frac{1}{x}$ of the work.

(B) In $y$ days, A does $\frac{y}{x}$ of the work.

(C) If A works for $x/2$ days, half of the work is done.

(D) If A works at half his efficiency, he takes $2x$ days to complete the work.

(E) Work done is inversely proportional to the number of days taken.

Question 2. A can do a work in 10 days and B can do the same work in 15 days. If they work together, which of the following are true?

(A) A's one day work = $1/10$.

(B) B's one day work = $1/15$.

(C) (A+B)'s one day work = $1/10 + 1/15 = 1/6$.

(D) They will complete the work together in 6 days.

(E) In 3 days, they complete half of the work.

Question 3. If A is twice as efficient as B, and B can do a work in 12 days, which of the following statements are true?

(A) A can do the work in 6 days.

(B) A's one day work = $1/6$.

(C) B's one day work = $1/12$.

(D) A and B together can do the work in 4 days.

(E) A and B together's one day work = $1/6 + 1/12 = 1/4$.

Question 4. A, B, and C can complete a work in 10, 12, and 15 days respectively. If they start working together, which of the following are true?

(A) Their individual one day works are $1/10, 1/12, 1/15$.

(B) Their combined one day work is $1/10 + 1/12 + 1/15 = 1/4$.

(C) They complete the work in 4 days.

(D) In 2 days, they complete half of the work.

(E) If A leaves after 2 days, B and C need to complete the remaining $1/2$ of the work.

Question 5. Pipe A can fill a tank in 20 minutes and pipe B can fill it in 30 minutes. Which of the following statements are true?

(A) In one minute, pipe A fills $1/20$ of the tank.

(B) In one minute, pipe B fills $1/30$ of the tank.

(C) If both are opened together, their combined filling rate is $1/20 + 1/30 = 1/12$ per minute.

(D) If both are opened together, they fill the tank in 12 minutes.

(E) In 6 minutes, they fill half of the tank together.

Question 6. Pipe A can fill a tank in 10 hours, and a leak B can empty it in 15 hours. If both are operating, which of the following are true?

(A) Pipe A's filling rate is $1/10$ per hour.

(B) Leak B's emptying rate is $1/15$ per hour.

(C) The net filling rate when both are open is $1/10 - 1/15 = 1/30$ per hour.

(D) It will take 30 hours to fill the tank if both are open.

(E) If the tank is half full, and both are open, it will take 15 more hours to fill it completely.

Question 7. 6 men can do a piece of work in 10 days. Which of the following are true (assuming constant work rate)?

(A) Total work = 60 man-days.

(B) 1 man can do the work in 60 days.

(C) 12 men can do the work in 5 days.

(D) The number of men and the number of days are in inverse variation.

(E) Work done is directly proportional to the number of men and days.

Question 8. 5 men or 10 women can complete a piece of work in 20 days. Which of the following statements are true?

(A) Work done by 5 men in 1 day = $1/20$ of the work.

(B) Work done by 1 man in 1 day = $1/(5 \times 20) = 1/100$ of the work.

(C) Work done by 1 woman in 1 day = $1/(10 \times 20) = 1/200$ of the work.

(D) 1 man is twice as efficient as 1 woman.

(E) 10 men and 20 women working together will complete the work in less than 10 days.

Question 9. A and B work alternately on a job, starting with A. A can complete the job alone in 10 days, and B can complete it alone in 20 days. Which of the following are true?

(A) A's one day work = $1/10$.

(B) B's one day work = $1/20$.

(C) Work done in the first two days (A+B) = $1/10 + 1/20 = 3/20$.

(D) The work will be completed in less than 15 days.

(E) The work will be completed in $13 \frac{1}{3}$ days.

Question 10. A and B undertake to complete a work for $\textsf{₹}300$. A can do the work in 6 days and B in 8 days. With the help of C, they complete it in 3 days. Which of the following are true about the distribution of money?

(A) A's one day work = $1/6$.

(B) B's one day work = $1/8$.

(C) (A+B+C)'s one day work = $1/3$.

(D) C's one day work = $1/3 - (1/6 + 1/8) = 1/24$.

(E) The money should be divided in the ratio of their one day work rates, i.e., $1/6 : 1/8 : 1/24$ or 4 : 3 : 1.

Question 11. Two pipes P and Q can fill a tank in 12 hours and 15 hours respectively. If both are opened together, which of the following is true?

(A) Their combined hourly rate is $1/12 + 1/15 = 9/60 = 3/20$.

(B) They will fill the tank in $20/3$ hours.

(C) They will fill the tank in $6 \frac{2}{3}$ hours.

(D) In 3 hours, they will fill $3 \times (3/20) = 9/20$ of the tank.

(E) If pipe Q is closed after 4 hours, the remaining work needs to be done by P.

Question 12. If 4 men and 5 women can complete a work in 10 days, and 5 men and 4 women can complete the same work in 8 days, which of the following statements are true about the efficiency of men and women?

(A) 40 man-days + 50 woman-days = Total Work.

(B) 40 man-days + 32 woman-days = Total Work.

(C) 50 woman-days = 32 woman-days.

(D) 50 woman-days - 32 woman-days = 40 man-days - 40 man-days.

(E) This problem can be solved to find the ratio of efficiency of a man to a woman.

Question 1. Which of the following are correct formulae relating Time (T), Speed (S), and Distance (D)?

(A) D = S $\times$ T

(B) S = D / T

(C) T = D / S

(D) T = S / D

(E) D = T / S

Question 2. Which of the following unit conversions are correct?

(A) 1 km/hr = $\frac{5}{18}$ m/s

(B) 1 m/s = $\frac{18}{5}$ km/hr

(C) 1 km = 1000 meters

(D) 1 hour = 60 minutes

(E) 1 minute = 60 seconds

Question 3. A car travels from A to B at speed $S_1$ and returns from B to A at speed $S_2$. Which of the following statements are true about the average speed for the round trip?

(A) Average speed = $\frac{S_1 + S_2}{2}$

(B) Average speed = $\frac{2 S_1 S_2}{S_1 + S_2}$

(C) Average speed is the harmonic mean of $S_1$ and $S_2$.

(D) If $S_1 = 40$ km/hr and $S_2 = 60$ km/hr, average speed = 48 km/hr.

(E) Average speed is always less than or equal to the arithmetic mean of $S_1$ and $S_2$.

Question 4. Two trains are moving. Which of the following statements about relative speed are true?

(A) If they move in the same direction with speeds $S_1$ and $S_2$ ($S_1 > S_2$), relative speed = $S_1 - S_2$.

(B) If they move in opposite directions with speeds $S_1$ and $S_2$, relative speed = $S_1 + S_2$.

(C) Relative speed is used when considering the time taken for one object to cross another.

(D) The distance to be covered when a train crosses a pole is the length of the train.

(E) The distance to be covered when a train crosses a platform is the length of the train.

Question 5. A train of length L meters passes a stationary object (like a pole or a man) in T seconds. Which of the following are true?

(A) Speed of the train = L / T m/s.

(B) The object is considered a point object.

(C) If the speed is in km/hr, it must be converted to m/s for the calculation.

(D) The length of the object needs to be considered.

(E) If the speed is $S$ km/hr, then $S \times \frac{5}{18} = \frac{L}{T}$.

Question 6. A train of length L1 meters passes another train of length L2 meters moving in the same direction with speeds $S_1$ and $S_2$ ($S_1 > S_2$). The time taken to cross is T seconds. Which of the following are true?

(A) The relative speed is $S_1 - S_2$.

(B) The total distance to be covered is L1 + L2.

(C) $T = \frac{L_1 + L_2}{S_1 - S_2}$ (where speeds are in appropriate units, e.g., m/s).

(D) If they move in opposite directions, the relative speed would be $S_1 + S_2$.

(E) The time taken is proportional to the relative speed.

Question 7. A boat's speed in still water is $V_b$ and the speed of the stream is $V_s$. Which of the following are true?

(A) Speed downstream = $V_b + V_s$.

(B) Speed upstream = $V_b - V_s$.

(C) $V_b = \frac{\text{Speed downstream} + \text{Speed upstream}}{2}$.

(D) $V_s = \frac{\text{Speed downstream} - \text{Speed upstream}}{2}$.

(E) The boat always travels faster downstream than upstream.

Question 8. In a race of D meters, if A beats B by $d_1$ meters, which of the following are true?

(A) When A covers D meters, B covers $D - d_1$ meters.

(B) The ratio of their speeds is $D : (D - d_1)$.

(C) The ratio of times taken to cover D meters is $(D - d_1) : D$.

(D) If A gives B a start of $d_1$ meters, they finish the race simultaneously if they run at their usual speeds.

(E) If A beats B by $t$ seconds, then B takes $t$ seconds more than A to complete the race.

Question 9. A person covers a distance in two parts. First part at speed $S_1$ for time $T_1$, second part at speed $S_2$ for time $T_2$. Which of the following are true?

(A) Total distance = $S_1 T_1 + S_2 T_2$.

(B) Total time = $T_1 + T_2$.

(C) Average speed = $\frac{S_1 T_1 + S_2 T_2}{T_1 + T_2}$.

(D) If $T_1 = T_2$, average speed = $\frac{S_1 + S_2}{2}$.

(E) If the distances covered are equal, average speed = $\frac{2 S_1 S_2}{S_1 + S_2}$.

Question 10. Two persons A and B start from the same point and move in the same direction. A's speed is $V_A$ and B's speed is $V_B$. Which of the following are true about the distance between them after time $t$?

(A) If $V_A > V_B$, the distance between them is $(V_A - V_B)t$.

(B) The relative speed is $V_A - V_B$.

(C) If they move in opposite directions, the distance between them after time $t$ is $(V_A + V_B)t$.

(D) If they move in opposite directions, the relative speed is $V_A + V_B$.

(E) Relative speed concepts apply when calculating when one object overtakes or meets another.

Question 11. A train crosses a platform 100 m long in 15 seconds and a pole in 5 seconds. Which of the following are true about the train?

(A) Let the length of the train be L and speed be S.

(B) $S = \frac{L}{5}$ (using pole information).

(C) $S = \frac{L+100}{15}$ (using platform information).

(D) The length of the train is 50 m.

(E) The speed of the train is 10 m/s.

Question 12. Excluding stoppages, the speed of a bus is 60 km/hr and including stoppages, it is 40 km/hr. Which of the following statements are true?

(A) The bus travels 60 km in 1 hour of running time.

(B) The bus covers 40 km in 1 hour of journey time (including stops).

(C) The time taken for stoppages in 1 hour is the time saved by travelling at the higher speed over the distance covered at the lower speed in 1 hour.

(D) Time for stoppage per hour = $\frac{\text{Difference in speeds}}{\text{Speed without stoppages}} \times 1 \text{ hour}$.

(E) The bus stops for 20 minutes per hour.

Question 13. A man rows 24 km downstream in 4 hours and 12 km upstream in 3 hours. Which of the following are true?

(A) Downstream speed = 6 km/hr.

(B) Upstream speed = 4 km/hr.

(C) Speed of man in still water = $\frac{6+4}{2} = 5$ km/hr.

(D) Speed of stream = $\frac{6-4}{2} = 1$ km/hr.

(E) He can row 10 km in still water in 2 hours.

Question 1. The average of a set of numbers is calculated by:

(A) Sum of the numbers divided by the number of quantities.

(B) $\frac{\sum x}{n}$ where $\sum x$ is the sum and $n$ is the count.

(C) The middle value when the numbers are arranged in order.

(D) The most frequently occurring number.

(E) Representing the central tendency of the data.

Question 2. The average of 5 numbers is 30. Which of the following statements are true?

(A) The sum of the 5 numbers is $5 \times 30 = 150$.

(B) If one number is removed, the sum becomes $150 - \text{removed number}$.

(C) If each number is increased by 5, the new average is $30 + 5 = 35$.

(D) If each number is multiplied by 2, the new average is $30 \times 2 = 60$.

(E) If a new number, 30, is added, the average remains 30.

Question 3. The average age of 10 students is 20 years. If a new student joins the class and the average age becomes 21 years, which of the following are true?

(A) Total age of 10 students = $10 \times 20 = 200$ years.

(B) Number of students becomes 11.

(C) New total age = $11 \times 21 = 231$ years.

(D) Age of the new student = $231 - 200 = 31$ years.

(E) The average increases because the new student is older than the original average.

Question 4. The average of 7 consecutive numbers is 25. Which of the following statements are true?

(A) The sum of the numbers is $7 \times 25 = 175$.

(B) The numbers are 22, 23, 24, 25, 26, 27, 28.

(C) The smallest number is 22.

(D) The largest number is 28.

(E) The average of any 7 consecutive numbers is the middle number.

Question 5. The average weight of 20 students is 50 kg. A student weighing 40 kg leaves the class. Which of the following statements are true about the remaining students?

(A) The new number of students is 19.

(B) The total weight of 20 students was $20 \times 50 = 1000$ kg.

(C) The total weight of the remaining 19 students is $1000 - 40 = 960$ kg.

(D) The new average weight is $960 / 19$ kg.

(E) The new average weight is greater than the original average.

Question 6. The average age of 5 members in a family is 30 years. If a new member is added, the average age increases by 2 years. Which of the following statements are true?

(A) Total age of 5 members = $5 \times 30 = 150$ years.

(B) Number of members becomes 6.

(C) New average age = $30 + 2 = 32$ years.

(D) New total age = $6 \times 32 = 192$ years.

(E) Age of the new member = $192 - 150 = 42$ years.

Question 7. In a group of 10 people, 5 have an average weight of 60 kg, and the remaining 5 have an average weight of 70 kg. Which of the following are true about the average weight of the entire group?

(A) The sum of weights of the first 5 people = $5 \times 60 = 300$ kg.

(B) The sum of weights of the remaining 5 people = $5 \times 70 = 350$ kg.

(C) Total weight of the 10 people = $300 + 350 = 650$ kg.

(D) Total number of students = $30 + 20 = 50$.

(E) Average weight of the entire group = $650 / 10 = 65$ kg.

Question 8. The average of first $n$ natural numbers is $\frac{n+1}{2}$. Which of the following statements are true based on this?

(A) The average of the first 10 natural numbers is 5.5.

(B) The sum of the first 10 natural numbers is 55.

(C) The average of the first 100 natural numbers is 50.5.

(D) The average increases as $n$ increases.

(E) This formula applies to any sequence of $n$ numbers.

Question 9. The average score of a batsman in 10 innings is 50. Which of the following are possible scores?

(A) 10 scores that sum up to 500.

(B) Scores like 40, 55, 60, 30, 50, 45, 70, 35, 50, 65.

(C) If he scores 100 runs in the 11th inning, his new average will be $\frac{500+100}{11}$.

(D) If he scores 100 runs in the 11th inning, his new average is $\frac{600}{11} \approx 54.55$.

(E) If his average in the first 5 innings was 40, his average in the next 5 innings was 60.

Question 10. In a class, there are 30 boys and 20 girls. The average marks of boys in a test are 70, and the average marks of girls are 80. Which of the following are true about the average marks of the entire class?

(A) Total marks of boys = $30 \times 70 = 2100$.

(B) Total marks of girls = $20 \times 80 = 1600$.

(C) Total marks of the class = $2100 + 1600 = 3700$.

(D) Total number of students = $30 + 20 = 50$.

(E) Average marks of the class = $3700 / 50 = 74$.

Question 11. A group consists of managers and workers. The average salary of 10 managers is $\textsf{₹}50000$, and the average salary of 50 workers is $\textsf{₹}20000$. Which of the following are true about the average salary of the entire group?

(A) Total salary of managers = $\textsf{₹}500000$.

(B) Total salary of workers = $\textsf{₹}1000000$.

(C) Total salary of the group = $\textsf{₹}1500000$.

(D) Total number of people = 60.

(E) Average salary of the group = $\textsf{₹}1500000 / 60 = \textsf{₹}25000$.

Question 12. The average of 6 numbers is 20. If two numbers are removed, the average of the remaining 4 numbers is 15. Which of the following statements are true?

(A) The sum of the 6 numbers is 120.

(B) The sum of the remaining 4 numbers is 60.

(C) The sum of the two removed numbers is $120 - 60 = 60$.

(D) The average of the two removed numbers is $60 / 2 = 30$.

(E) The values of the two removed numbers must be 30 and 30.

Question 1. Which of the following statements are true about the speeds of the hands of a clock?

(A) The minute hand completes one revolution in 60 minutes.

(B) The minute hand moves $6^\circ$ per minute.

(C) The hour hand completes one revolution in 12 hours.

(D) The hour hand moves $0.5^\circ$ per minute.

(E) The relative speed of the minute hand with respect to the hour hand is $5.5^\circ$ per minute.

Question 2. At 12 o'clock, the hour hand and minute hand coincide. Which of the following statements are true about the hands of a clock?

(A) The hands coincide 11 times in 12 hours.

(B) The hands coincide 22 times in 24 hours.

(C) The hands are opposite to each other 11 times in 12 hours.

(D) The hands are at right angles 22 times in 12 hours.

(E) The hands are at right angles 44 times in 24 hours.

Question 3. To find the time when the hands of a clock are at a specific angle $\theta$ between $H$ and $H+1$ o'clock, the general formula for minutes past H is often used: $M = \frac{2}{11} |30H \pm \theta|$. Which of the following applications of this formula are correct?

(A) To find when hands coincide, set $\theta = 0^\circ$.

(B) To find when hands are opposite, set $\theta = 180^\circ$.

(C) To find when hands are at right angles, set $\theta = 90^\circ$.

(D) For right angles, there are usually two times between any two hours (except 2-3 and 8-9). The $\pm$ sign gives these two times.

(E) The angle is measured clockwise from the hour hand to the minute hand.

Question 4. A clock gains 5 minutes in every hour. If it is set right at 12 noon, what can be said about the time it shows later?

(A) It shows more time than the correct time.

(B) It gains 120 minutes in 24 hours.

(C) In 1 hour (correct time), the faulty clock shows 65 minutes (faulty time).

(D) 60 minutes of correct time = 65 minutes of faulty time.

(E) 1 minute of correct time = $65/60 = 13/12$ minutes of faulty time.

Question 5. A clock loses 2 minutes in every hour. If it is set right at 12 noon, what can be said about the time it shows later?

(A) It shows less time than the correct time.

(B) It loses 48 minutes in 24 hours.

(C) In 1 hour (correct time), the faulty clock shows 58 minutes (faulty time).

(D) 60 minutes of correct time = 58 minutes of faulty time.

(E) 1 minute of correct time = $58/60 = 29/30$ minutes of faulty time.

Question 6. The minute hand overtakes the hour hand at intervals of approximately $65 \frac{5}{11}$ minutes of correct time. If a clock's hands overtake each other at intervals of exactly 65 minutes, which of the following is true?

(A) The clock is running fast.

(B) The clock is gaining time.

(C) In 65 minutes of correct time, the faulty clock shows $65 \frac{5}{11}$ minutes.

(D) The gain in 65 minutes is $65 \frac{5}{11} - 65 = \frac{5}{11}$ minutes.

(E) The gain per hour can be calculated from this information.

Question 7. At what time between 5 and 6 o'clock are the hands of a clock in a straight line (opposite)?

(A) Using $M = \frac{2}{11} |30 \times 5 \pm 180|$.

(B) This simplifies to $M = \frac{2}{11} |150 \pm 180|$.

(C) Taking the $+$ sign gives $M = \frac{2}{11} (150 + 180) = \frac{2}{11} \times 330 = 60$. So, 6:00.

(D) Taking the $-$ sign gives $M = \frac{2}{11} |150 - 180| = \frac{2}{11} |-30| = \frac{60}{11} = 5 \frac{5}{11}$. So, $5: 5 \frac{5}{11}$.

(E) Both 5: $5 \frac{5}{11}$ and 6:00 are times between 5 and 6 o'clock when hands are opposite.

Question 8. What is the angle between the hour hand and minute hand at 7:20?

(A) Angle covered by hour hand from 12 = $30H + M/2 = 30 \times 7 + 20/2 = 210 + 10 = 220^\circ$.

(B) Angle covered by minute hand from 12 = $6M = 6 \times 20 = 120^\circ$.

(C) The angle between them is $|220^\circ - 120^\circ| = 100^\circ$.

(D) The angle is $100^\circ$.

(E) The reflex angle is $360^\circ - 100^\circ = 260^\circ$.

Question 9. How many times are the hands of a clock at right angles between 6 AM and 6 PM?

(A) In 12 hours, they are at right angles 22 times.

(B) The interval from 6 AM to 6 PM is exactly 12 hours.

(C) The times 3:00, 9:00, 15:00 (3:00 PM), 21:00 (9:00 PM) are right angle times.

(D) Within any hour interval, there are two right angle instances, except between 2-3 and 8-9 where there is only one.

(E) Therefore, in 12 hours, there are $12 \times 2 - 2 = 22$ right angle instances.

Question 10. The time shown on a clock is 9:30. What is the angle between the hands?

(A) Hour hand position from 12 = $30 \times 9 + 30/2 = 270 + 15 = 285^\circ$.

(B) Minute hand position from 12 = $6 \times 30 = 180^\circ$.

(C) The angle between them is $|285^\circ - 180^\circ| = 105^\circ$.

(D) The angle is $105^\circ$.

(E) The reflex angle is $360^\circ - 105^\circ = 255^\circ$.

Question 11. At what time between 10 and 11 o'clock will the hands of a clock coincide?

(A) Using $M = \frac{2}{11} |30 \times 10 \pm 0|$.

(B) $M = \frac{2}{11} \times 300 = \frac{600}{11} = 54 \frac{6}{11}$.

(C) The time is $10: 54 \frac{6}{11}$.

(D) This is the only time between 10 and 11 when the hands coincide.

(E) The hands coincide exactly at 12:00.

Question 12. A clock gains 10 seconds in 3 hours. Which of the following are true?

(A) It gains $10/3$ seconds per hour.

(B) It gains $10/3 \times 24 = 80$ seconds per day.

(C) It gains $1 \frac{1}{3}$ minutes per day.

(D) In 24 hours (correct time), the faulty clock shows $24 \text{ hours } + 80 \text{ seconds}$.

(E) The faulty clock is faster than the correct clock.

Question 13. A clock gains 5 minutes in every hour. If it is set right at 12 noon, what can be said about the time it shows later?

(A) It shows more time than the correct time.

(B) It gains 120 minutes in 24 hours.

(C) In 1 hour (correct time), the faulty clock shows 65 minutes (faulty time).

(D) 60 minutes of correct time = 65 minutes of faulty time.

(E) 1 minute of correct time = $65/60 = 13/12$ minutes of faulty time.

Question 14. A clock loses 2 minutes in every hour. If it is set right at 12 noon, what can be said about the time it shows later?

(A) It shows less time than the correct time.

(B) It loses 48 minutes in 24 hours.

(C) In 1 hour (correct time), the faulty clock shows 58 minutes (faulty time).

(D) 60 minutes of correct time = 58 minutes of faulty time.

(E) 1 minute of correct time = $58/60 = 29/30$ minutes of faulty time.

Question 15. The minute hand overtakes the hour hand at intervals of approximately $65 \frac{5}{11}$ minutes of correct time. If a clock's hands overtake each other at intervals of exactly 65 minutes, which of the following is true?

(A) The clock is running fast.

(B) The clock is gaining time.

(C) In 65 minutes of correct time, the faulty clock shows $65 \frac{5}{11}$ minutes.

(D) The gain in 65 minutes is $65 \frac{5}{11} - 65 = \frac{5}{11}$ minutes.

(E) The gain per hour can be calculated from this information.

Question 16. At what time between 5 and 6 o'clock are the hands of a clock in a straight line (opposite)?

(A) Using $M = \frac{2}{11} |30 \times 5 \pm 180|$.

(B) This simplifies to $M = \frac{2}{11} |150 \pm 180|$.

(C) Taking the $+$ sign gives $M = \frac{2}{11} (150 + 180) = \frac{2}{11} \times 330 = 60$. So, 6:00.

(D) Taking the $-$ sign gives $M = \frac{2}{11} |150 - 180| = \frac{2}{11} |-30| = \frac{60}{11} = 5 \frac{5}{11}$. So, $5: 5 \frac{5}{11}$.

(E) Both 5: $5 \frac{5}{11}$ and 6:00 are times between 5 and 6 o'clock when hands are opposite.

Question 17. What is the angle between the hour hand and minute hand at 7:20?

(A) Angle covered by hour hand from 12 = $30H + M/2 = 30 \times 7 + 20/2 = 210 + 10 = 220^\circ$.

(B) Angle covered by minute hand from 12 = $6M = 6 \times 20 = 120^\circ$.

(C) The angle between them is $|220^\circ - 120^\circ| = 100^\circ$.

(D) The angle is $100^\circ$.

(E) The reflex angle is $360^\circ - 100^\circ = 260^\circ$.

Question 18. How many times are the hands of a clock at right angles between 6 AM and 6 PM?

(A) In 12 hours, they are at right angles 22 times.

(B) The interval from 6 AM to 6 PM is exactly 12 hours.

(C) The times 3:00, 9:00, 15:00 (3:00 PM), 21:00 (9:00 PM) are right angle times.

(D) Within any hour interval, there are two right angle instances, except between 2-3 and 8-9 where there is only one.

(E) Therefore, in 12 hours, there are $12 \times 2 - 2 = 22$ right angle instances.

Question 19. The time shown on a clock is 9:30. What is the angle between the hands?

(A) Hour hand position from 12 = $30 \times 9 + 30/2 = 270 + 15 = 285^\circ$.

(B) Minute hand position from 12 = $6 \times 30 = 180^\circ$.

(C) The angle between them is $|285^\circ - 180^\circ| = 105^\circ$.

(D) The angle is $105^\circ$.

(E) The reflex angle is $360^\circ - 105^\circ = 255^\circ$.

Question 20. At what time between 10 and 11 o'clock will the hands of a clock coincide?

(A) Using $M = \frac{2}{11} |30 \times 10 \pm 0|$.

(B) $M = \frac{2}{11} \times 300 = \frac{600}{11} = 54 \frac{6}{11}$.

(C) The time is $10: 54 \frac{6}{11}$.

(D) This is the only time between 10 and 11 when the hands coincide.

(E) The hands coincide exactly at 12:00.

Question 21. A clock gains 10 seconds in 3 hours. Which of the following are true?

(A) It gains $10/3$ seconds per hour.

(B) It gains $10/3 \times 24 = 80$ seconds per day.

(C) It gains $1 \frac{1}{3}$ minutes per day.

(D) In 24 hours (correct time), the faulty clock shows $24 \text{ hours } + 80 \text{ seconds}$.

(E) The faulty clock is faster than the correct clock.

Question 1. Which of the following years are leap years?

(A) 1947

(B) 1950

(C) 2000

(D) 2024

(E) 2100

Question 2. An ordinary year has 365 days. A leap year has 366 days. Which of the following are true about odd days?

(A) An ordinary year has 1 odd day ($365 = 52 \times 7 + 1$).

(B) A leap year has 2 odd days ($366 = 52 \times 7 + 2$).

(C) Odd days are the extra days beyond a complete week.

(D) The day of the week repeats every 7 days.

(E) The concept of odd days helps in determining the day of the week for a given date.

Question 3. Which of the following are correct about the number of odd days in century years?

(A) 100 years have 5 odd days.

(B) 200 years have 3 odd days.

(C) 300 years have 1 odd day.

(D) 400 years have 0 odd days.

(E) The pattern of odd days in century years repeats every 400 years.

Question 4. If 1st January of a year is a Monday, which of the following are true?

(A) If it's an ordinary year, 31st December of that year is also a Monday.

(B) If it's an ordinary year, 1st January of the next year is a Tuesday.

(C) If it's a leap year, 31st December of that year is a Tuesday.

(D) If it's a leap year, 1st January of the next year is a Wednesday.

(E) In a leap year, there is an extra day (Feb 29th), adding one extra odd day.

Question 5. Which of the following months have 30 days?

(A) April

(B) June

(C) September

(D) November

(E) February

Question 6. If 14th July 2007 was a Saturday, which of the following statements are true?

(A) 14th July 2008 was a Sunday (2008 is a leap year, Feb 29th falls between the dates).

(B) 14th July 2008 was a Monday.

(C) The year 2007 has 1 odd day.

(D) The year 2008 has 2 odd days.

(E) 14th July 2009 was a Tuesday (2008 is a leap year, adding 2 days).

Question 7. The calendar of which of the following years will repeat the calendar of 2011?

(A) 2017 (Add 6 years, as 2011 is an ordinary year after a leap year)

(B) 2022 (Add 11 years)

(C) 2012

(D) 2014

(E) 2011 calendar repeats after adding a total number of years such that the sum of odd days is a multiple of 7.

Question 8. If today is Thursday, what will be the day of the week after 200 days?

(A) $200 = 28 \times 7 + 4$.

(B) There are 4 odd days.

(C) The day will be 4 days after Thursday.

(D) The day will be Sunday.

(E) The day will be Monday.

Question 9. Which of the following are correct about the number of odd days in months?

(A) January (31 days) has 3 odd days.

(B) February (28 or 29 days) has 0 or 1 odd day.

(C) March (31 days) has 3 odd days.

(D) April (30 days) has 2 odd days.

(E) May (31 days) has 3 odd days.

Question 10. Which of the following century years are leap years?

(A) 400

(B) 800

(C) 1200

(D) 1600

(E) 2000

Question 11. Which of the following statements are true about the repetition of calendars?

(A) An ordinary year calendar repeats after 6 years or 11 years or 11 years ...

(B) A leap year calendar repeats after 28 years.

(C) The pattern of adding years (6, 11, 11, 28) is based on the accumulation of odd days.

(D) The calendar for the year after a leap year (like 2013 after 2012) repeats after 6 years.

(E) The calendar for the second year after a leap year (like 2014 after 2012) repeats after 11 years.

Question 12. If 1st March 2020 was a Sunday, what day was 1st March 2021?

(A) Monday (2020 is a leap year)

(B) Tuesday (Feb 29th is included between the dates)

(C) Tuesday (2020 is a leap year, adding 2 odd days).

(D) $366/7$ has a remainder of 2.

(E) The day shifts forward by 2 days because 2020 is a leap year and Feb 29th is between March 1 2020 and March 1 2021.

Question 1. Six friends P, Q, R, S, T, U are sitting in a row facing North. R is second to the right of Q. S is at the extreme left end and is third to the left of T. Q is not sitting at an extreme end. Which of the following statements are true based on this arrangement?

(A) The order from left to right is S _ Q _ R _ T.

(B) Since S is at the extreme left and third to the left of T, the positions are S _ _ T _ _.

(C) Q is not at an extreme end, so Q is somewhere in the middle.

(D) If R is second to the right of Q, and Q is not at an end, possible arrangements for Q and R are _ Q _ R _.

(E) Combining S _ _ T _ _ and _ Q _ R _, and considering Q not at an end, the arrangement must be S P Q U R T.

Question 2. Seven people A, B, C, D, E, F, G are sitting in a circle facing the center. D is second to the right of G, who is to the immediate right of C. B is to the immediate left of F. E is not an immediate neighbour of D or F. Which of the following are true about the arrangement?

(A) The sequence C - G - D exists in the circle (clockwise or anti-clockwise).

(B) The sequence F - B exists (clockwise or anti-clockwise).

(C) E is not next to D or F.

(D) The arrangement (clockwise from C) is C - G - D - A - E - B - F.

(E) A is to the immediate right of D.

Question 3. Five boys A, B, C, D, E are sitting in a row. A is between C and D. B is to the right of D. E is between B and C. Which of the following statements are true?

(A) A is to the immediate left of D.

(B) C is to the immediate left of A.

(C) D is to the immediate left of B.

(D) C is to the immediate left of E.

(E) The order from left to right is C E B D A.

Question 4. Six girls G1, G2, G3, G4, G5, G6 are sitting around a circular table facing outwards. G2 is sitting two places to the left of G5. G4 is sitting to the immediate right of G2. G1 is sitting opposite to G4. G3 is not an immediate neighbour of G5. Which of the following are true?

(A) If G2 is at a position, G5 is two positions clockwise from G2.

(B) The sequence G2 - G4 exists in the circle (clockwise from G2).

(C) G1 is directly across from G4.

(D) G3 is not next to G5.

(E) The arrangement (clockwise starting from G1) is G1 - G3 - G2 - G4 - G6 - G5.

Question 5. Eight friends A, B, C, D, E, F, G, H are sitting around a square table, four at corners facing the center and four in the middle of the sides facing outside. G sits at a corner and is an immediate neighbour of A. D sits in the middle of a side and faces A. C sits opposite to D. B is not an immediate neighbour of A or D. H sits in the middle of a side. E is not an immediate neighbour of G. Which of the following are true?

(A) G and A are at adjacent corners.

(B) A is at a corner facing center.

(C) D is in the middle of a side facing outside, facing A (at a corner).

(D) C is also in the middle of a side facing outside.

(E) The arrangement (starting from G at a corner, clockwise) could be G A E F D C H B.

Question 6. In a queue, A is 15th from the front and B is 20th from the back. If there are 10 persons between A and B, which of the following are true?

(A) The total number of persons is $15 + 20 + 10 = 45$.

(B) A is 11 positions ahead of the first person between A and B.

(C) B is 10 positions behind the last person between A and B.

(D) The order is Front ... A ... 10 persons ... B ... Back.

(E) The total number of persons is 45.

Question 7. Five people are sitting in a row. P is to the left of Q, but on the right of S. R is on the right of Q, but on the left of T. Which of the following statements are true?

(A) The sequence S ... P ... Q ... R ... T exists.

(B) P is between S and Q.

(C) R is between Q and T.

(D) The possible arrangement from left to right is S P Q R T.

(E) Q is sitting exactly in the middle.

Question 8. In a row of 40 girls, Rina is 15th from the left and Mona is 28th from the right. Which of the following statements are true?

(A) Rina's position from the right is $40 - 15 + 1 = 26$th.

(B) Mona's position from the left is $40 - 28 + 1 = 13$th.

(C) Rina is to the right of Mona in the row.

(D) The number of girls between Rina and Mona is $26 - 28 - 1$ (since positions cross over).

(E) The number of girls between Rina (15th from left) and Mona (13th from left) is $15 - 13 - 1 = 1$.

Question 9. Six persons A, B, C, D, E, F are sitting around a round table. A is between E and D. C is between B and F. E is to the right of F. Which of the following are true about the arrangement?

(A) The sequence E - A - D exists (clockwise or anti-clockwise).

(B) The sequence B - C - F exists (clockwise or anti-clockwise).

(C) E is immediately clockwise from F.

(D) The arrangement (clockwise from A) is A D F E B C.

(E) B is opposite to D.

Question 10. Twelve people are sitting in two parallel rows, 6 in each row. Row 1 (North facing): A, B, C, D, E, F. Row 2 (South facing): P, Q, R, S, T, U. F sits opposite to R. B is at one of the extreme ends. C is second to the left of E. The person opposite to D is second to the right of Q. Which of the following are true?

(A) The arrangement is likely solvable given enough conditions.

(B) F and R are facing each other.

(C) C and E are in Row 1, with C two places to the left of E.

(D) D is in Row 1. The person opposite D is in Row 2.

(E) Q is in Row 2.

Question 11. In a linear arrangement puzzle, the term "immediate neighbour" means:

(A) The person sitting directly next to someone on either side.

(B) The person sitting opposite in a circular or square arrangement.

(C) The person sitting two places away.

(D) The person whose position is adjacent.

(E) Can refer to the person on the left or the right (unless a direction is specified).

Question 12. In a circular arrangement problem where all persons are facing the center, "X is second to the right of Y" means:

(A) Starting from Y, move one position clockwise, then another position clockwise to reach X.

(B) There is one person sitting between Y and X when moving clockwise from Y.

(C) The positions are Y, _, X (clockwise or anti-clockwise).

(D) If Y is at position 1, X is at position 3 (assuming clockwise movement).

(E) The term "right" refers to the person's own right side when facing the center.

Question 1. In an Alligation and Mixture problem, if two ingredients are mixed in a certain ratio to form a mixture, which of the following principles are applied?

(A) The cost of the mixture lies between the costs of the two ingredients.

(B) The ratio of the quantities of the two ingredients is inversely proportional to the difference between their costs and the mean cost.

(C) Rule of Alligation diagram helps in finding the ratio of quantities.

(D) If quantity of ingredient 1 is $Q_1$ at cost $C_1$, and quantity of ingredient 2 is $Q_2$ at cost $C_2$, and the mixture cost is $C_m$, then $Q_1 C_1 + Q_2 C_2 = (Q_1 + Q_2) C_m$.

(E) This method is only applicable to costs, not other properties like percentages or concentrations.

Question 2. A bag contains coins of different denominations. If the ratio of the number of coins is given, and the total value is known, which of the following can be determined?

(A) The value contributed by each denomination.

(B) The total number of coins.

(C) The number of coins of each denomination.

(D) The average value per coin.

(E) The total weight of the coins.

Question 3. If the population of a town changes by successive percentage increases or decreases, which of the following are true?

(A) The final population can be calculated by multiplying the initial population by the successive multipliers.

(B) If the rate is $r_1\%$ increase followed by $r_2\%$ increase, the total percentage increase is $r_1 + r_2 + \frac{r_1 r_2}{100}$.

(C) If the rate is $r_1\%$ increase followed by $r_2\%$ decrease, the total percentage change is $r_1 - r_2 - \frac{r_1 r_2}{100}$.

(D) The order of successive changes matters for the final value (e.g., +10% then -10% is different from -10% then +10%).

(E) This is an application of compound percentage change.

Question 4. In a partnership business, profits are typically shared in the ratio of investments and the time for which the investments are made. If A invests $\textsf{₹}I_A$ for $T_A$ time and B invests $\textsf{₹}I_B$ for $T_B$ time, and the total profit is P, which of the following are true?

(A) The ratio of their profit shares is $(I_A \times T_A) : (I_B \times T_B)$.

(B) A's share of profit = $P \times \frac{I_A T_A}{I_A T_A + I_B T_B}$.

(C) If the investments are for the same time period, profits are shared in the ratio of investments.

(D) If the profits are shared equally, the investments must be equal (assuming same time). If time is different, $I_A T_A = I_B T_B$.

(E) Salaries given to partners are deducted from the profit before distributing the remaining profit.

Question 5. A mixture of milk and water has a certain ratio. If water is added, which of the following statements are true?

(A) The amount of milk remains constant.

(B) The amount of water increases.

(C) The total quantity of the mixture increases.

(D) The ratio of milk to water decreases.

(E) The percentage of milk in the mixture decreases.

Question 6. Simple Interest and Compound Interest concepts can be applied in which of the following real-world scenarios?

(A) Calculating interest on savings accounts.

(B) Calculating interest on loans.

(C) Calculating the growth of investments over time.

(D) Calculating the amount of tax on goods sold.

(E) Estimating population growth or decline.

Question 7. Time and Work problems often involve concepts of work rate. If a person's work rate is constant, which of the following statements are true?

(A) Work done is directly proportional to the time spent.

(B) The number of persons doing a job is inversely proportional to the time taken (if work done is fixed).

(C) If A completes a work in $x$ days, their daily work rate is $1/x$.

(D) Total work is often considered as 1 unit or a common multiple of individual times.

(E) If multiple people work together, their individual work rates are added to find the combined work rate.

Question 8. Time, Speed, and Distance problems are based on the fundamental relationship Speed = Distance / Time. Which of the following are important considerations when solving these problems?

(A) Ensuring consistent units for speed, distance, and time.

(B) Using relative speed when objects are moving towards or away from each other.

(C) Considering the length of objects (like trains) when they cross poles, platforms, or other trains.

(D) Average speed for multiple segments of a journey is the simple average of speeds.

(E) Boats and streams problems involve calculating speeds relative to water flow (upstream/downstream).

Question 9. Averages are used to represent a typical value in a set of data. Which of the following statements are true about averages?

(A) Adding a value equal to the current average to the set does not change the average.

(B) Adding a value greater than the current average increases the average.

(C) Multiplying each number in the set by a constant multiplies the average by the same constant.

(D) The average of a set of numbers is always one of the numbers in the set.

(E) Weighted average is used when different data points have different levels of importance or frequency.

Question 10. Problems involving Clocks and Calendars often require understanding relative speeds and the concept of odd days. Which of the following are true?

(A) The minute hand moves faster than the hour hand.

(B) The angle between the hands of a clock changes constantly.

(C) Leap years occur every 4 years, except for century years not divisible by 400.

(D) The number of odd days determines the shift in the day of the week over a period.

(E) Calculating angles or finding times when hands are in specific positions involves considering their speeds and relative speeds.

Question 11. Arrangement problems (linear or circular) require logical deduction based on given positional clues. Which of the following are helpful techniques?

(A) Drawing diagrams to represent the positions.

(B) Identifying fixed positions or extreme ends first.

(C) Using relative positions (left/right, opposite, between).

(D) Eliminating possibilities based on constraints.

(E) Assuming a starting position in circular arrangements if no fixed point is given (and adjusting if necessary).

Question 12. Commercial Arithmetic problems often involve combining concepts like profit/loss, discount, and taxes. Which of the following are true?

(A) Profit/Loss is typically calculated on the Cost Price (CP).

(B) Discount is typically calculated on the Marked Price (MP).

(C) Selling Price (SP) can be calculated as MP - Discount or CP + Profit.

(D) Taxes (like GST) are usually added to the price of the goods or services.

(E) The final price paid by the customer includes all applicable taxes and is after any discounts.