Matching Items MCQs for Sub-Topics of Topic 3: Quantitative Aptitude

(i) Ratio of 50 paise to $\textsf{₹}2$

(ii) Simplest form of the ratio 25 : 40

(iii) Ratio of 1 hour to 30 minutes

(iv) Simplest form of the ratio $1/2 : 1/3$

(v) Ratio of the number of days in February (ordinary year) to March

(a) 2 : 1

(b) 3 : 2

(c) 1 : 4

(d) 28 : 31

(e) 5 : 8

(i) Direct Proportion

(ii) Inverse Proportion

(iii) Mean Proportional between $a$ and $c$

(iv) Third Proportional to $a$ and $b$

(v) Product of extremes equals product of means property

(a) $b^2 = ac$

(b) $\frac{x}{y} = k$ (constant)

(c) $\frac{x}{y} = \frac{1}{k}$ (constant)

(d) $a : b :: b : c$ where $c$ is the proportional

(e) For $a:b :: c:d$, $ad = bc$

(i) If cost of 10 pens is $\textsf{₹}100$, find cost of 15 pens

(ii) If 5 workers finish a job in 20 days, find days for 8 workers

(iii) If a car travels 150 km in 3 hours, find time for 400 km

(iv) If $\textsf{₹}500$ is earned in 2 days, find earnings in 7 days

(v) If 3 kg apples cost $\textsf{₹}240$, find quantity for $\textsf{₹}400$

(a) Cost per day

(b) Days per worker

(c) Time per km

(d) Quantity per Rupee

(e) Cost per pen

(i) Dividing a sum of money in a given ratio

(ii) Comparing speeds of two vehicles

(iii) Finding a proportional value when two ratios are equal

(iv) Finding the average of quantities

(v) Calculating work done by a group of people

(a) Average calculation

(b) Proportion application

(c) Unitary Method application

(d) Ratio simplification

(e) Sharing in ratio

(i) If $a:b = 2:1$ and $b:c = 1:3$, then $a:b:c = $

(ii) If 5 is the mean proportional between 1 and $x$, then $x = $

(iii) If 6, $x$, 24 are in continued proportion, then $x = $

(iv) If 20 men can do a work in 10 days, 25 men can do it in

(v) If cost of 5 pencils is $\textsf{₹}25$, cost of 1 pencil is

(a) $\textsf{₹}5$

(b) 8 days

(c) 12

(d) 25

(e) 2 : 1 : 3

(i) Direct Variation

(ii) Inverse Variation

(iii) Joint Variation

(iv) $y = kx$

(v) $y = k/x$

(a) $y \propto 1/x$

(b) $y \propto x$

(c) Equation for inverse variation

(d) $z \propto xy$

(e) Equation for direct variation

(i) Cost of goods and quantity purchased

(ii) Speed of a car and time taken for a fixed distance

(iii) Number of workers and time taken for a fixed job

(iv) Distance covered and time taken at constant speed

(v) Area of a square and side length squared

(a) Inverse Variation

(b) Direct Variation

(i) Constant of variation, $k$

(ii) Value of $y$ when $x=12$

(iii) Value of $x$ when $y=30$

(iv) Equation relating $y$ and $x$

(v) Graph of $y$ vs $x$

(a) Straight line through origin

(b) 60

(c) $y = 2x$

(d) 15

(e) 2

(i) Constant of variation, $k$

(ii) Value of $a$ when $b=10$

(iii) Value of $b$ when $a=15$

(iv) Equation relating $a$ and $b$

(v) Graph of $a$ vs $b$ (for $a,b > 0$)

(a) $a = 30/b$

(b) 3

(c) 2

(d) 30

(e) Hyperbola

(i) $y \propto x^2$

(ii) $p \propto 1/\sqrt{q}$

(iii) $z \propto x/y$

(iv) $V = \frac{4}{3}\pi r^3$

(v) Force of gravity $\propto$ product of masses / distance squared

(a) Combined Variation

(b) Direct variation with square

(c) Direct variation with cube

(d) Inverse square law in physics

(e) Inverse variation with square root

(i) 25%

(ii) 50%

(iii) 75%

(iv) 100%

(v) 10%

(a) 1/4

(b) 0.5

(c) 3/4

(d) 1

(e) 1/10

(i) 10% of 500

(ii) 20% of 100

(iii) 50% of 150

(iv) 75% of 80

(v) 1% of 1000

(a) 10

(b) 20

(c) 50

(d) 60

(e) 75

(i) Increase from 50 to 60

(ii) Decrease from 80 to 60

(iii) Increase from 40 to 50

(iv) Decrease from 100 to 90

(v) Increase from 200 to 250

(a) 20% increase

(b) 25% increase

(c) 25% decrease

(d) 10% decrease

(e) 20% increase

(i) 10% increase followed by 10% increase

(ii) 20% increase followed by 20% increase

(iii) 10% increase followed by 10% decrease

(iv) 20% increase followed by 20% decrease

(v) 20% increase followed by 10% decrease

(a) 44% increase

(b) 1% decrease

(c) 4% decrease

(d) 11% increase

(e) 8% increase

(i) Percentage

(ii) Percentage Increase

(iii) Percentage Decrease

(iv) Finding a quantity given its percentage

(v) Successive Percentage Change formula

(a) $\frac{\text{Decrease}}{\text{Original}} \times 100$

(b) Per hundred

(c) $\frac{\text{Increase}}{\text{Original}} \times 100$

(d) Final Value = Original Value $\times (1 + r_1/100) \times (1 + r_2/100) \times ...$

(e) Quantity = Given Value $\times \frac{100}{\text{Given Percentage}}$

(i) Cost Price (CP)

(ii) Selling Price (SP)

(iii) Marked Price (MP)

(iv) Profit

(v) Loss

(a) The price at which an article is bought

(b) The price at which an article is sold

(c) The excess of SP over CP

(d) The reduction on the MP

(e) The price printed on the article

(f) The excess of CP over SP

(i) Profit Percentage

(ii) Loss Percentage

(iii) Discount

(iv) SP when profit % is known

(v) CP when loss % is known

(a) $\text{MP} - \text{SP}$

(b) $\frac{\text{Loss}}{\text{CP}} \times 100$

(c) $\text{CP} \times \frac{100 + \text{Profit}%}{100}$

(d) $\frac{\text{Profit}}{\text{CP}} \times 100$

(e) $\text{SP} \times \frac{100}{100 - \text{Loss}%}$

(i) CP = $\textsf{₹}800$, Profit = 20%, SP =

(ii) CP = $\textsf{₹}600$, Loss = 10%, SP =

(iii) MP = $\textsf{₹}1200$, Discount = 10%, SP =

(iv) SP = $\textsf{₹}1500$, Profit = 25%, CP =

(v) SP = $\textsf{₹}900$, Loss = 10%, CP =

(a) $\textsf{₹}1000$

(b) $\textsf{₹}1100$

(c) $\textsf{₹}1200$

(d) $\textsf{₹}1080$

(e) $\textsf{₹}540$

(f) $\textsf{₹}960$

(i) Profit %

(ii) Loss %

(iii) Discount %

(iv) Marked Price (MP)

(v) Selling Price (SP)

(a) Base for calculating discount

(b) Base for calculating profit/loss %

(c) Price after adding profit to CP

(d) Price after subtracting loss from CP

(e) MP with or without discount

(i) Successive discounts of 10% and 20%

(ii) Gain of 10% and loss of 10% on the same SP

(iii) Marked up by 20%, discounted by 10% on MP

(iv) Cost of 10 articles = SP of 8 articles

(v) Using 900g weight for 1 kg while selling at CP

(a) $11 \frac{1}{9} \%$ gain

(b) 25% gain

(c) 28% discount

(d) 1% loss

(e) 8% gain

(i) Simple Interest Formula

(ii) Compound Interest Formula (Annual)

(iii) Amount under Simple Interest

(iv) Amount under Compound Interest (Annual)

(v) Difference between CI and SI for 2 years

(a) $P \left(1 + \frac{R}{100}\right)^T$

(b) $P + SI$

(c) $\frac{P \times R \times T}{100}$

(d) $\frac{PR^2}{100^2}$

(e) $P \left(1 + \frac{R}{100}\right)^n$ (where n is number of periods)

(i) Interest calculated on principal only

(ii) Interest calculated on principal and accumulated interest

(iii) Growth of population at a fixed percentage per year

(iv) Depreciation of a machine value annually

(v) Interest earned is same for every period

(a) Compound Interest (with negative rate)

(b) Simple Interest

(c) Compound Interest

(d) Simple Interest Characteristic

(e) Neither SI nor CI

(i) Compounded Half-yearly

(ii) Compounded Quarterly

(iii) Compounded Monthly

(iv) Compounded Annually

(v) Effective annual rate for R% nominal compounded half-yearly

(a) Rate R, Time T periods

(b) Rate R/12, Time 12T periods

(c) Rate R/4, Time 4T periods

(d) Rate R/2, Time 2T periods

(e) $\left[\left(1 + \frac{R/2}{100}\right)^2 - 1\right] \times 100$

(i) SI on $\textsf{₹}1000$ at 5% for 3 years

(ii) Amount for SI on $\textsf{₹}2000$ at 10% for 2 years

(iii) Rate if $\textsf{₹}500$ becomes $\textsf{₹}600$ in 4 years SI

(iv) Time if $\textsf{₹}1000$ becomes $\textsf{₹}1300$ at 10% SI

(v) Principal if SI is $\textsf{₹}240$ at 8% for 5 years

(a) $\textsf{₹}600$

(b) $\textsf{₹}2400$

(c) 3 years

(d) 5%

(e) $\textsf{₹}150$

(i) CI on $\textsf{₹}10000$ at 10% for 2 years (annual)

(ii) Amount on $\textsf{₹}10000$ at 10% for 2 years (annual)

(iii) CI on $\textsf{₹}20000$ at 10% for 1 year (half-yearly)

(iv) Amount on $\textsf{₹}20000$ at 10% for 1 year (half-yearly)

(v) Difference between CI and SI on $\textsf{₹}1000$ at 10% for 3 years

(a) $\textsf{₹}31$

(b) $\textsf{₹}12100$

(c) $\textsf{₹}2100$

(d) $\textsf{₹}22050$

(e) $\textsf{₹}2050$

(i) CGST

(ii) SGST

(iii) IGST

(iv) UTGST

(v) CGST + SGST/UTGST

(a) Inter-state supply

(b) Intra-state supply

(c) Tax collected by Central Government

(d) Tax collected by State Government

(e) Tax collected by Union Territory Government

(i) Price before GST = $\textsf{₹}1000$, GST 18%, Final Price =

(ii) Final Price = $\textsf{₹}1180$ (includes 18% GST), Price before GST =

(iii) Price before GST = $\textsf{₹}5000$, GST 12% (intra-state), CGST amount =

(iv) Price before GST = $\textsf{₹}5000$, GST 12% (intra-state), SGST amount =

(v) Price before GST = $\textsf{₹}5000$, GST 12% (inter-state), IGST amount =

(a) $\textsf{₹}600$

(b) $\textsf{₹}1180$

(c) $\textsf{₹}2500$

(d) $\textsf{₹}300$

(e) $\textsf{₹}1000$

(f) $\textsf{₹}300$

(i) Sales Tax (pre-GST)

(ii) Value Added Tax (VAT)

(iii) Goods and Services Tax (GST)

(iv) Income Tax

(v) Customs Duty

(a) Tax on income

(b) Tax on import/export

(c) Multi-stage tax with ITC, consumption-based

(d) Single point tax on sale of goods

(e) Tax on value added at each stage, with set-off

(i) Input Tax Credit (ITC)

(ii) Tax Incidence

(iii) Tax Base

(iv) Exclusive of Tax

(v) Inclusive of Tax

(a) The price includes the tax amount

(b) The price does not include the tax amount

(c) The point on which tax is levied

(d) Credit for tax paid on inputs

(e) The final burden of the tax

(i) Base Price $\textsf{₹}2000$, GST 5%

(ii) Base Price $\textsf{₹}5000$, GST 12%

(iii) Base Price $\textsf{₹}10000$, GST 18%

(iv) Base Price $\textsf{₹}15000$, GST 28%

(v) Final Price $\textsf{₹}1200$ (includes 20% Sales Tax), Sales Tax amount =

(a) $\textsf{₹}2700$

(b) $\textsf{₹}100$

(c) $\textsf{₹}600$

(d) $\textsf{₹}4200$

(e) $\textsf{₹}200$

(i) Daily work rate is $1/10$

(ii) Daily work rate is $1/20$

(iii) Combined daily work rate of A ($1/10$) and B ($1/20$)

(iv) Combined daily work rate of A ($1/10$), B ($1/12$), C ($1/15$)

(v) Daily work rate implies work done in one day

(a) Work completed in 4 days

(b) Work completed in 20 days

(c) Work completed in 10 days

(d) $3/20$ of work per day

(e) $1/4$ of work per day

(i) A takes 10 days, B takes 15 days. Together they take

(ii) A takes 20 days. B is twice as efficient as A. B takes

(iii) A & B together take 12 days. A alone takes 20 days. B alone takes

(iv) 6 men take 8 days. 12 men take

(v) Pipe A fills in 10 hours, Pipe B empties in 15 hours. Together they fill in

(a) 10 days

(b) 6 days

(c) 30 days

(d) 4 days

(e) 30 hours

(i) A + B working together

(ii) Pipe filling + Pipe emptying

(iii) Men and Women working together

(iv) A, B, C working together

(v) Work done by A in $x$ days

(a) Sum of individual daily works

(b) Sum of individual daily works (considering their number)

(c) Difference of filling and emptying rates

(d) $x \times (\text{A's daily work})$

(e) Sum of individual hourly rates

(i) A takes 20 days, B takes 30 days. They work together for 6 days. Work done =

(ii) A takes 10 days. After 4 days, A's work done = $4/10 = 2/5$

(iii) A & B together take 8 days. After 4 days, work left = $1/2$

(iv) A, B, C take 10, 12, 15 days. They work together for 2 days. Work left = $1 - (2/10+2/12+2/15) = 1 - 2(1/4) = 1/2$

(v) A takes 15 days. He works for 5 days. Fraction of work done = $1/3$

(a) $1/3$

(b) $1/2$

(c) $4/10 = 2/5$

(d) $6/20 + 6/30 = 1/3 + 1/5 = 8/15$

(e) $1 - (2/10+2/12+2/15) = 1 - 2(1/4) = 1/2$

(i) Inlet Pipe A fills in 12 min, Inlet Pipe B fills in 18 min. Together they fill in

(ii) Inlet Pipe fills in 8 hours, Leak empties in 12 hours. Together they fill in

(iii) Pipe A fills in 20 min, Pipe B empties in 30 min. Together they fill in

(iv) Pipe A fills in 6 hours, B in 8 hours, C in 24 hours. Together they fill in

(v) Tank fills in 10 hours, but takes 15 hours due to leak. Leak empties in

(a) 4 hours

(b) 30 minutes

(c) 36 min

(d) 24 hours

(e) 24 min

(i) Speed

(ii) Distance

(iii) Time

(iv) 1 km/hr in m/s

(v) 1 m/s in km/hr

(a) Distance / Speed

(b) Distance / Time

(c) Speed $\times$ Time

(d) $5/18$ m/s

(e) $18/5$ km/hr

(i) Two objects moving in the same direction with speeds $S_1, S_2$ ($S_1 > S_2$)

(ii) Two objects moving in opposite directions with speeds $S_1, S_2$

(iii) Train crossing a stationary pole

(iv) Train crossing a stationary platform

(v) Train crossing a man walking in the same direction

(a) Relative speed = $S_1 + S_2$

(b) Relative speed = Train speed

(c) Distance = Train length

(d) Distance = Train length + Platform length

(e) Relative speed = $S_1 - S_2$

(i) Speed Downstream

(ii) Speed Upstream

(iii) Speed of boat in still water ($V_b$)

(iv) Speed of stream ($V_s$)

(v) Time taken upstream for distance D

(a) $V_b - V_s$

(b) $V_b + V_s$

(c) $\frac{\text{Downstream speed} + \text{Upstream speed}}{2}$

(d) $\frac{\text{Downstream speed} - \text{Upstream speed}}{2}$

(e) $D / (V_b - V_s)$

(i) Travel from A to B at $S_1$ and B to A at $S_2$

(ii) Travel at $S_1$ for time $T_1$ and at $S_2$ for time $T_2$

(iii) Travel at $S_1$ for distance $D_1$ and at $S_2$ for distance $D_2$

(iv) Travel at $S_1$ for time $T$ and at $S_2$ for same time $T$

(v) Travel at $S_1$ for distance $D$ and at $S_2$ for same distance $D$

(a) $\frac{D_1 + D_2}{D_1/S_1 + D_2/S_2}$

(b) $\frac{S_1 T_1 + S_2 T_2}{T_1 + T_2}$

(c) $\frac{S_1 + S_2}{2}$

(d) $\frac{2 S_1 S_2}{S_1 + S_2}$

(e) $\frac{2 S_1 S_2}{S_1 + S_2}$

(i) Car speed 60 km/hr, time 3 hours, distance =

(ii) Distance 300 km, speed 50 km/hr, time =

(iii) Train length 100m, crosses pole in 5s, speed in m/s =

(iv) Train length 150m, platform 250m, crosses in 20s, speed in m/s =

(v) Boat speed still water 10 km/hr, stream 2 km/hr, speed downstream =

(a) 12 km/hr

(b) 20 m/s

(c) 6 hours

(d) 180 km

(e) 20 m/s

(i) 2, 4, 6, 8, 10

(ii) 1, 2, 3, 4, 5, 6

(iii) 10, 20, 30, 40

(iv) 5, 5, 5, 5, 5

(v) First 5 prime numbers (2, 3, 5, 7, 11)

(a) 3.5

(b) 5

(c) 5.6

(d) 6

(e) 25

(i) Average of $N$ numbers is $A$. A new number $x$ is added. New average = $(NA + x) / (N+1)$

(ii) Average of $N$ numbers is $A$. A number $x$ is removed. New average = $(NA - x) / (N-1)$

(iii) Average of $N$ numbers is $A$. A number $x$ is replaced by $y$. Change in average = $(y-x)/N$

(iv) Average of Group 1 ($N_1$ items, Avg A1) and Group 2 ($N_2$ items, Avg A2). Combined average = $(N_1 A_1 + N_2 A_2) / (N_1 + N_2)$

(v) Average of first half and second half results overlapping at the middle term

(a) Calculating the new average after addition

(b) Calculating the new average after removal

(c) Finding the middle term

(d) Calculating the change in average after replacement

(e) Calculating a weighted average

(i) Average of 10 numbers is 20. If each number is increased by 3, new average is

(ii) Average of 5 numbers is 25. If one number 35 is removed, new average is

(iii) Average of 6 persons is 50 kg. A person weighing 70 kg replaces one weighing 60 kg. New average is

(iv) Average of 5 innings is 40. Score in 6th inning is 70. New average after 6 innings is

(v) Average age of 30 students is 15 years. Teacher's age is 45 years. New average (including teacher) is

(a) 16 years

(b) 48 kg

(c) 45 kg

(d) 22.5

(e) 23

(i) Simple Average

(ii) Weighted Average

(iii) Average of consecutive numbers

(iv) Average of first $N$ natural numbers

(v) Effect of adding/removing a value on average

(a) $\frac{N(N+1)/2}{N} = \frac{N+1}{2}$

(b) Sum of products of values and weights divided by sum of weights

(c) Average changes based on relation of added/removed value to old average

(d) Simple arithmetic mean

(e) The middle value

(i) Average of first 5 odd numbers (1, 3, 5, 7, 9)

(ii) Average of first 5 even numbers (2, 4, 6, 8, 10)

(iii) Average of first 5 multiples of 3 (3, 6, 9, 12, 15)

(iv) Average of 5 consecutive integers with middle number 10

(v) Average of 5 consecutive integers starting with 10

(a) 12

(b) 9

(c) 5

(d) 6

(e) 10

(i) Minute hand in 1 minute

(ii) Hour hand in 1 minute

(iii) Minute hand in 5 minutes

(iv) Hour hand in 1 hour

(v) Hour hand in 12 hours

(a) $0.5^\circ$

(b) $30^\circ$

(c) $6^\circ$

(d) $360^\circ$

(e) $30^\circ$

(i) 3:00

(ii) 6:00

(iii) 12:00

(iv) 9:00

(v) 3:30

(a) $0^\circ$

(b) $90^\circ$

(c) $180^\circ$

(d) $90^\circ$

(e) $75^\circ$

(i) Coincide

(ii) Opposite

(iii) At right angles

(iv) In a straight line (coincide or opposite)

(v) Overtakes the hour hand

(a) 11 times

(b) 22 times

(c) 22 times

(d) 11 times

(e) 11 times

(i) Clock gains time

(ii) Clock loses time

(iii) Minute hand overtakes hour hand in less than $65 \frac{5}{11}$ minutes

(iv) Minute hand overtakes hour hand in more than $65 \frac{5}{11}$ minutes

(v) Set right at a certain time, shows incorrect time later

(a) Faulty clock

(b) Clock is fast

(c) Clock is slow

(d) Clock loses time

(e) Clock gains time

(i) Relative speed of minute hand with respect to hour hand

(ii) Time taken for hands to coincide after 12:00

(iii) Time taken for hands to be opposite after 6:00

(iv) Time taken for hands to be at right angles after 3:00

(v) Total gain/loss of a faulty clock in 24 hours compared to correct time

(a) $5.5^\circ$ per minute

(b) Related to the rate of gain or loss per hour

(c) $65 \frac{5}{11}$ minutes

(d) $32 \frac{8}{11}$ minutes

(e) $32 \frac{8}{11}$ minutes

(i) 7 days

(ii) 365 days (Ordinary Year)

(iii) 366 days (Leap Year)

(iv) 30 days

(v) 31 days

(a) 1 odd day

(b) 0 odd days

(c) 2 odd days

(d) 3 odd days

(e) 2 odd days

(i) 100 years

(ii) 200 years

(iii) 300 years

(iv) 400 years

(v) 5 years (ordinary years)

(a) 1 odd day

(b) 0 odd days

(c) 3 odd days

(d) 5 odd days

(e) 5 odd days

(i) Ordinary Year

(ii) Leap Year

(iii) Century Year

(iv) Leap Century Year

(v) Calendar repetition for a leap year

(a) Divisible by 400

(b) 2 odd days

(c) Divisible by 100

(d) 1 odd day

(e) Repeats after 28 years

(i) 100 years odd days

(ii) 200 years odd days

(iii) 300 years odd days

(iv) 400 years odd days

(v) Last day of a century cannot be

(a) Friday

(b) Wednesday

(c) Monday

(d) Sunday or Tuesday or Thursday

(e) Tuesday

(i) 7 days difference

(ii) 14 days difference

(iii) 365 days difference

(iv) 366 days difference

(v) 60 days difference

(a) Same day

(b) Shifts by 1 day forward

(c) Shifts by 2 days forward

(d) Shifts by 4 days forward ($60 \div 7$, remainder 4)

(e) Same day

(i) Linear Arrangement

(ii) Circular Arrangement

(iii) Immediate Neighbour

(iv) Facing the Center (in circular)

(v) Facing Outside (in circular)

(a) Left/Right are standard

(b) Right is clockwise, Left is anti-clockwise

(c) Right is anti-clockwise, Left is clockwise

(d) Arrangement in a straight line

(e) Person adjacent to

(f) Arrangement in a circle

(i) A is second to the right of B

(ii) A is third to the left of B

(iii) A is fourth to the right of B

(iv) A is immediately right of B

(v) A is between B and C

(a) 0 persons

(b) 1 person

(c) 2 persons

(d) 3 persons

(e) Can be 1 or more

(i) A is opposite B ($N$=6)

(ii) A is opposite B ($N$=7)

(iii) A is second to the right of B ($N$=5)

(iv) A is third to the left of B ($N$=8)

(v) A is immediate left of B ($N$=4)

(a) 1 person

(b) No direct opposite

(c) 3 persons (on either side)

(d) 2 persons

(e) 0 persons

(i) Rank 10th from the top

(ii) Rank 25th from the top

(iii) Rank 1st from the top

(iv) Rank 50th from the top

(v) Rank 30th from the top

(a) 50th from bottom

(b) 41st from bottom

(c) 26th from bottom

(d) 1st from bottom

(e) 21st from bottom

(i) "X is between Y and Z"

(ii) "P is third to the right of Q"

(iii) "A and B are immediate neighbours"

(iv) "C is at an extreme end"

(v) "D is opposite to E"

(a) Fixes position in linear ends

(b) Establishes adjacency

(c) Establishes relative positions with fixed number of persons between

(d) Establishes relative positions (could be immediate or with others in between)

(e) Establishes positions directly across from each other (circular/square)

(i) Mixing two quantities with different properties (e.g., price, concentration)

(ii) Sharing profit in a business among partners

(iii) Calculating the final population after successive growth/decline rates

(iv) Finding an unknown value based on the average of a group

(v) Problems involving work done by multiple individuals or groups

(a) Time and Work principles

(b) Partnership principles

(c) Successive percentage change

(d) Alligation and Mixture

(e) Average calculations

(i) Finding the price of a mixture given the prices and ratio of components

(ii) Calculating the share of profit for each partner based on investment and time

(iii) Determining the total income given total expenditure and savings

(iv) Finding the time taken for multiple pipes to fill or empty a tank

(v) Calculating the original salary before a percentage increase

(a) Percentage concepts

(b) Alligation or weighted average

(c) Income, Expenditure, Savings relation

(d) Pipes and Cisterns (Time and Work application)

(e) Partnership calculations

(i) Calculating tax payable on goods

(ii) Determining the time when clock hands are together

(iii) Finding the day of the week for a future date

(iv) Calculating the speed of a boat in a river

(v) Determining the sitting arrangement of people around a table

(a) Boats and Streams

(b) Calendar rules (Odd days)

(c) Commercial Arithmetic (Taxes)

(d) Clock problems (Relative speed of hands)

(e) Arrangement/Puzzle solving

(i) Ratio of milk and water in a 50L mixture ($3:2$ milk:water)

(ii) Profit share of A from $\textsf{₹}10000$ profit (A:B investment $2:3$ for same time)

(iii) Average speed for a round trip (to city @ 40 km/hr, back @ 60 km/hr)

(iv) Time taken for A (10 days) and B (15 days) to work together

(v) SI on $\textsf{₹}5000$ @ 10% for 2 years

(a) $\textsf{₹}1000$

(b) 6 days

(c) 48 km/hr

(d) $\textsf{₹}4000$

(e) 30L milk, 20L water

(i) Sum if SI for 3 years is $\textsf{₹}300$ and CI for 2 years is $\textsf{₹}210$ (Rate is same)

(ii) Time taken for 4 men and 6 women to complete a work if 1 man $= 2$ women and 8 men take 10 days

(iii) Distance upstream if boat speed = 10 km/hr, stream = 2 km/hr, total time for 60 km downstream & upstream is 12 hours

(iv) New average if average of 10 students is 40 and one student (40 kg) leaves

(v) Price before GST if price including 18% GST is $\textsf{₹}5900$

(a) $\textsf{₹}5000$

(b) 40

(c) $\textsf{₹}5000$

(d) 8 days

(e) 24 km