Here is a curated set of 30 questions on Ratio and Proportion, complete with an answer key,

detailed solutions, and links to relevant video concepts.

Ratio and Proportion Practice Questions

Level 1 (Easy)
Question 1: If a : b = 2 : 3 and b : c = 5 : 7, then what is the ratio c : a? (a) 15:21 (b) 20:21 (c)
21:10 (d) 10:21
Question 2: Two numbers are in the ratio P : Q. When 1 is added to both the numerator and the
denominator, the ratio gets changed to R/S. Again, when 1 is added to both the numerator and
the denominator, it becomes 1/2. [cite_start]Find the sum of P and Q. (a) 3 (b) 4 (c) 5 (d) 6
Question 3: ` 3650 is divided among 4 engineers, 3 MBAs and 5 CAs such that 3 CAs get as
much as 2 MBAs and 3 Engineers as much as 2 CAs. [cite_start]Find the share of an MBA. (a)
300 (b) 450 (c) 475 (d) None of these
[cite_start]Question 4: If 3 examiners can examine a certain number of answer books in 10
days by working 4 hours a day, for how many hours a day would 4 examiners have to work in
order to examine thrice the number of answer books in 30 days? (a) 3 (b) 1 (c) 8 (d) 6
[cite_start]Question 5: In a mixture of 60 litres, the ratio of milk and water is 2 : 3. How much
water must be added to this mixture so that the ratio of milk and water becomes 1 : 2? (a) 10
litres (b) 12 litres (c) 15 litres (d) 20 litres
[cite_start]Question 6: The incomes of P and Q are in the ratio 1: 2 and their expenditures are
in the ratio 1: 3. If each saves 500, then, P’s income can
be:[span_4](start_span)[span_4](end_span) (a) 1000 (b) 1500 (c) 3000 (d) `2000
[cite_start]Question 7: A number is mistakenly divided by 2 instead of being multiplied by 2.
Find the percentage change in the result due to this mistake. (a) 100% (b) 125% (c) 200% (d)
75%
Question 8: The population of a town is 5,00,000. The rate of increase is 20% per annum.
[cite_start]Find the population at the start of the third year. (a) 6,20,000 (b) 7,20,000 (c) 8,30,000
(d) None of these.
Question 9: A and B start a business. A invests 1,00,000 for 4 months and B invests 40,000 for
a year. The ratio of their profits is: (a) 5:6 (b) 6:5 (c) 5:7 (d) 7:5
Question 10: The ratio of the monthly incomes of A and B is 11:13 and the ratio of their
expenditures is 9:11. [cite_start]If both of them manage to save 4,000 per month, then find the
difference in their incomes (in `). (a) 2,500 (b) 3,200 (c) 4,000 (d) 3,000

This file is made by rojgardekhlo.com

Level 2 (Moderate)
[cite_start]Question 11: The ratio of water and milk in a 30 litre mixture is 7 : 3. Find the quantity
of water to be added to the mixture in order to make this ratio 6 : 1. (a) 30 (b) 32 (c) 33 (d) 35
[cite_start]Question 12: Four numbers in the ratio 1:2 : 4 : 8 add up to give a sum of 120. Find
the value of the biggest number. (a) 40 (b) 30 (c) 64 (d) 60
[cite_start]Question 13: A mixture contains milk and water in the ratio 3 : 1. On adding 5 litres of
water, the ratio of milk to water becomes 2 : 1. The quantity of milk in the mixture is: (a) 15 litres
(b) 25 litres (c) 32.5 litres (d) 30 litres
Question 14: Two alloys of aluminium have different percentages of aluminium in them. The
first one weighs 8 kg and the second one weighs 16 kg. One piece each of equal weight was cut
off from both the alloys and the first piece was alloyed with the second alloy and the second
piece alloyed with the first one. As a result, the percentage of aluminium became the same in
the resulting two new alloys. [cite_start]What was the weight of each cut-off piece? (a) 5.33 kg
(b) 4 kg (c) 4.66 kg (d) 5 kg
Question 15: A milkman mixes 20 liters of water with 80 liters of milk. After selling one-fourth of
this mixture, he adds water to replenish the quantity that he had sold. [cite_start]What is the
current proportion of water to milk? (a) 2 : 3 (b) 1 : 2 (c) 1 : 3 (d) 3 : 4
[cite_start]Question 16: A precious stone weighing 35 grams worth 12,250 is accidentally
dropped and gets broken into two pieces having weights in the ratio of 2 : 5. If the price varies
as the square of the weight then find the loss
incurred.[span_13](start_span)[span_13](end_span) (a) 5750 (b) 6000 (c) 5500 (d) ` 5000
Question 17: A container has 40 litres of milk. Then, 4 litres are removed from the container
and replaced with 4 litres of water. This process of replacing 4 litres of the liquid in the container
with an equal volume of water is continued repeatedly. [cite_start]The smallest number of times
of doing this process, after which the volume of milk in the container becomes less than that of
water, is? (a) 6 (b) 7 (c) 5 (d) 8
Question 18: Soham's initial expenditure and savings were in the ratio of 5:3. His income
increases by 25%. [cite_start]If his initial savings were 4,500, find his income (in `) after the
increment. (a) 16000 (b) 15000 (c) 9375 (d) 12000
[cite_start]Question 19: Two numbers A and B are such that the sum of 5% of A and 10% of B
is 1/2 of the sum of 20% of A and 10% of B. Find the ratio of A:B? (a) 1:1 (b) 1:2 (c) 2:1 (d) 3:1
Question 20: The ratio of the monthly incomes of A and B is 4: 5 respectively. Ratio of monthly
savings of A and B is 14:19 respectively. [cite_start]If the monthly expenditure of A and B is
1200 each, then what is the difference between the monthly incomes of A and B? (a) 2000 (b)
4000 (c) 1000 (d) 5000

This file is made by rojgardekhlo.com

Level 3 (Hard)
Question 21: Three quantities A, B, C are such that AB = KC, where k is a constant. When A is
kept constant, B varies directly as C; when B is kept constant, A varies directly as C and when C
is kept constant, A varies inversely as B. Initially, A was at 5 and A:B:C was 1:3:5.
[cite_start]Find the value of A when B equals 9 at constant C. (a) 8 (b) 8.33 (c) 9 (d) 9.5
Question 22: Three containers A, B and C are having mixtures of milk and water in the ratio of
1 : 5, 3 : 5 and 5 : 7, respectively. [cite_start]If the capacities of the containers are in the ratio 5 :
4 : 5, find the ratio of milk to water, if the mixtures of all the three containers are mixed together.
(a) 53:115 (b) 53:116 (c) 54:115 (d) 54:116
Question 23: A, B and C get into a partnership for a year by investing 3000, 4000 and 5000
respectively. A is a working partner and gets 10% of the total profit for his work and the
remaining profit is divided among them in the ratio of their investments. If the profit A gets is
360, what is the total profit? (a) 1000 (b) 1200 (c) 900 (d) 1500
Question 24: A dishonest shopkeeper mixed 1 litre of water for every 3 litres of petrol and thus
made up 36 litres of petrol. [cite_start]If he now adds 15 litres of petrol to the mixture, find the
ratio of petrol and water in the new mixture. (a) 12: 5 (b) 14: 3 (c) 7: 2 (d) 9: 4
Question 25: Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to
catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the
train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km
per hour. It is known that C is located between west and northwest of B, with BC at 60o to AB.
Also, C is located between south and south west of A with AC at 30o to AB. [cite_start]The
latest time by which Rahim must leave A and still catch the train is closest to (a) 6:15 am (b)
6:30 am (c) 6:45 am (d) 7:00 am
[cite_start]Question 26: If a certain amount of money is divided equally among n persons, each
one receives 352. However, if two persons receive 506 each and the remaining amount is
divided equally among the other persons, each of them receive less than or equal to ` 330.
Then, the maximum possible value of n is (a) 16 (b) 14 (c) 12 (d) 18
Question 27: Jayant bought a certain number of white shirts at the rate of 1,000 per piece and
a certain number of blue shirts at the rate of 1,125 per piece. For each shirt, he then set a fixed
market price which was 25% higher than the average cost of all the shirts. He sold all the shirts
at a discount of 10% and made a total profit of ` 51,000. [cite_start]If he bought both colours of
shirts, then the maximum possible total number of shirts that he could have bought is (a) 400 (b)
404 (c) 407 (d) 410
Question 28: Three men and eight machines can finish a job in half the time taken by three
machines and eight men to finish the same job. [cite_start]If two machines can finish the job in
13 days, then how many men can finish the job in 13 days? (a) 13 (b) 10 (c) 11 (d) 12
[cite_start]Question 29: In a village, the ratio of number of males to females is 5 : 4. The ratio of
number of literate males to literate females is 2 : 3. The ratio of the number of illiterate males to
illiterate females is 4 : 3. If 3600 males in the village are literate, then the total number of
females in the village is: (a) 43200 (b) 44000 (c) 45000 (d) 46500
Question 30: A mixture is prepared by mixing two solutions P and Q. While one litre of solution
P weighs 0.9 kg, one litre of solution Q weighs 760 gram. [cite_start]If half litre of the mixture
weighs 436 grams, then the percentage of solution P in the mixture, in terms of volume, equals
(a) 80 (b) 60 (c) 70 (d) 65

This file is made by rojgardekhlo.com

Answer Key
Level 1
1.​ (c) 2. (c) 3. (b) 4. (a) 5. (b) 6. (a) 7. (d) 8. (b) 9. (a) 10. (c)

Level 2
1.​ (c) 12. (c) 13. (d) 14. (a) 15. (a) 16. (d) 17. (b) 18. (b) 19. (a) 20. (c)

Level 3
1.​ (b) 22. (a) 23. (c) 24. (b) 25. (b) 26. (a) 27. (c) 28. (a) 29. (a) 30. (b)
This file is made by rojgardekhlo.com
Detailed Solutions
Level 1 (Easy)
1. Solution: Given a : b = 2 : 3 and b : c = 5 : 7. To find a : b : c, we need to make the value of
'b' common in both ratios. LCM of 3 and 5 is 15. a : b = 2 : 3 = (2 * 5) : (3 * 5) = 10 : 15 b : c = 5 :
7 = (5 * 3) : (7 * 3) = 15 : 21 So, a : b : c = 10 : 15 : 21. We need to find c : a, which is 21 : 10.
Video Solution: Watch a similar problem on YouTube
2. Solution: Let the initial ratio be P/Q. After adding 1 to both, the ratio is (P+1)/(Q+1) = R/S.
After adding 1 again, the ratio is (P+2)/(Q+2) = 1/2. This means 2(P+2) = Q+2, so 2P + 4 = Q +
2, which simplifies to Q = 2P + 2. We can test the options for P+Q. If P+Q = 5 (Option c), and P
and Q are integers, possible pairs are (1,4) and (2,3). If P=1, Q=4, then Q = 2(1) + 2 = 4. This
fits the condition. Let's check: (1+2)/(4+2) = 3/6 = 1/2. Video Solution: Watch a similar problem
on YouTube
3. Solution: Let E, M, and C be the shares of an engineer, an MBA, and a CA respectively. We
are given: 3C = 2M and 3E = 2C. From this, we get M = 1.5C and E = (2/3)C. The total amount
is distributed among 4 engineers, 3 MBAs, and 5 CAs. So, 4E + 3M + 5C = 3650. Substituting
the values of E and M in terms of C: 4(2/3)C + 3(1.5)C + 5C = 3650 (8/3)C + 4.5C + 5C = 3650
(8/3 + 9/2 + 5)C = 3650 ((16+27+30)/6)C = 3650 (73/6)C = 3650 => C = 300. Share of an MBA,
M = 1.5 * 300 = 450. Video Solution: Watch a similar problem on YouTube
4. Solution: This is a work and time problem, which can be solved using the formula: M1 * D1 *
H1 / W1 = M2 * D2 * H2 / W2. Here, M = Men, D = Days, H = Hours, W = Work. Given: M1=3,
D1=10, H1=4, W1=1 (let's assume the work is 1 unit). M2=4, D2=30, H2=?, W2=3 (thrice the
work). (3 * 10 * 4) / 1 = (4 * 30 * H2) / 3 120 = 40 * H2 => H2 = 3 hours. Video Solution: Watch
a similar problem on YouTube
5. Solution: Initial mixture = 60 litres. Ratio of milk to water = 2:3. Milk = (2/5) * 60 = 24 litres.
Water = (3/5) * 60 = 36 litres. Let 'x' litres of water be added. The new mixture will have 24 litres
of milk and (36+x) litres of water. The new ratio is 1:2. So, 24 / (36+x) = 1/2 48 = 36 + x => x =
12 litres. Video Solution: Watch a similar problem on YouTube
6. Solution: Let the incomes of P and Q be I_p and I_q, and their expenditures be E_p and
E_q. I_p / I_q = 1/2 and E_p / E_q = 1/3. Savings = Income - Expenditure. So, I_p - E_p = 500
and I_q - E_q = 500. From the ratios, I_q = 2I_p and E_q = 3E_p. Substitute these into the
second savings equation: 2I_p - 3E_p = 500. We have a system of two linear equations:
1.​ I_p - E_p = 500
2.​ 2I_p - 3E_p = 500 Multiply the first equation by 3: 3I_p - 3E_p = 1500. Subtract the
second equation from this: (3I_p - 3E_p) - (2I_p - 3E_p) = 1500 - 500 => I_p = 1000.
Video Solution: Watch a similar problem on YouTube
7. Solution: Let the number be 'x'. The correct result should be 2x. The result obtained is x/2.
The change in the result is 2x - x/2 = 3x/2. The percentage change is (change in result / original
result) * 100 = ((3x/2) / 2x) * 100 = (3/4) * 100 = 75%. Video Solution: Watch a similar problem
on YouTube
8. Solution: Population at the start = 5,00,000. After the first year (increase of 20%), population
= 5,00,000 * 1.20 = 6,00,000. After the second year (increase of 20%), population = 6,00,000 *
1.20 = 7,20,000. The population at the start of the third year is 7,20,000. Video Solution: Watch
a similar problem on YouTube
9. Solution: This is a partnership problem. The ratio of profits is the ratio of the product of
investment and time. A's investment = 1,00,000 for 4 months. B's investment = 40,000 for 12
months. Ratio of profits = (1,00,000 * 4) : (40,000 * 12) = 4,00,000 : 4,80,000 = 40:48 = 5:6.
Video Solution: Watch a similar problem on YouTube
10. Solution: Let the incomes of A and B be 11x and 13x, and their expenditures be 9y and 11y.
Savings = Income - Expenditure. So, 11x - 9y = 4000 and 13x - 11y = 4000. We have 11x - 9y =
13x - 11y => 2y = 2x => y = x. Substitute y=x into the first equation: 11x - 9x = 4000 => 2x =
4000 => x = 2000. Incomes are 112000 = 22000 and 132000 = 26000. The difference is 4000.
Video Solution: Watch a similar problem on YouTube

This file is made by rojgardekhlo.com