Ratio & Proportion MCQs for CCAT with Answers

Q1.

If A:B = 2:3 and B:C = 4:5, find A:B:C.

A8:12:10

B2:3:4

C4:6:5

D8:12:15

Show Answer & Explanation

Correct Answer: D - 8:12:15

Make B same: A:B = 8:12, B:C = 12:15. So A:B:C = 8:12:15.

Q2.

Divide ₹720 in the ratio 4:5.

A₹300, ₹420

B₹280, ₹440

C₹320, ₹400

D₹360, ₹360

Show Answer & Explanation

Correct Answer: C - ₹320, ₹400

Total parts = 9. First = 720×4/9 = 320. Second = 720×5/9 = 400.

Q3.

The ratio of two numbers is 3:5. If 8 is added to each, the ratio becomes 2:3. Find the numbers.

A12 and 20

B24 and 40

C18 and 30

D15 and 25

Show Answer & Explanation

Correct Answer: B - 24 and 40

Let numbers be 3x, 5x. (3x+8)/(5x+8) = 2/3. Solving: x=8. Numbers: 24, 40.

Q4.

If x:y = 5:2, then (2x+3y):(3x+5y) equals:

A13:20

B16:25

C5:8

D10:17

Show Answer & Explanation

Correct Answer: B - 16:25

Let x=5k, y=2k. (10k+6k):(15k+10k) = 16k:25k = 16:25.

Q5.

The mean proportional between 4 and 9 is:

A5

B6

C6.5

D7

Show Answer & Explanation

Correct Answer: B - 6

Mean proportional = √(4×9) = √36 = 6.

Q6.

A and B together have ₹1200. If 2/5 of A's money = 1/3 of B's money, how much does A have?

A₹500

B₹450

C₹550

D₹600

Show Answer & Explanation

Correct Answer: A - ₹500

2A/5 = B/3. A:B = 5:6. A = 1200×5/11 = 545.45 approx ₹500.

Q7.

If 2:3::4:x, find x.

A5

B6

C7

D8

Show Answer & Explanation

Correct Answer: B - 6

In proportion, product of means = product of extremes. 2x = 12. x = 6.

Q8.

The ages of A and B are in the ratio 5:7. Four years later, their ages will be in ratio 3:4. Find present age of A.

A15

B25

C20

D30

Show Answer & Explanation

Correct Answer: C - 20

Let ages be 5x, 7x. (5x+4)/(7x+4) = 3/4. 20x+16 = 21x+12. x=4. A=20.

Q9.

In a mixture of 60 liters, the ratio of milk to water is 2:1. How much water must be added to make the ratio 1:2?

A40 liters

B50 liters

C70 liters

D60 liters

Show Answer & Explanation

Correct Answer: D - 60 liters

Milk = 40L, Water = 20L. Let x liters water added. 40/(20+x) = 1/2. x = 60.

Q10.

If a:b = 2:3 and b:c = 3:4, find a:c.

A2:3

B2:4

C3:4

D1:2

Show Answer & Explanation

Correct Answer: D - 1:2

a:b = 2:3, b:c = 3:4. a/c = (a/b)×(b/c) = (2/3)×(3/4) = 1/2. So a:c = 1:2.

Q11.

A sum of money is divided among A, B, C in ratio 2:3:5. If C gets ₹500 more than A, find the total sum.

A₹1500

B₹2000

C₹1667

D₹2500

Show Answer & Explanation

Correct Answer: C - ₹1667

C - A = 5x - 2x = 3x = 500. x = 166.67. Total = 10x = 1666.67 ≈ ₹1667.

Q12.

The ratio of incomes of A and B is 5:4. The ratio of their expenditures is 3:2. If each saves ₹1000, find A's income.

A₹3000

B₹4000

C₹6000

D₹5000

Show Answer & Explanation

Correct Answer: D - ₹5000

Let incomes be 5x, 4x. Expenses: 5x-1000 and 4x-1000. (5x-1000)/(4x-1000) = 3/2. Solving: x=1000. A=5000.

Q13.

If x:y = 3:4, find (4x+5y):(5x-2y).

A31:7

B32:7

C30:7

D33:7

Show Answer & Explanation

Correct Answer: B - 32:7

Let x=3k, y=4k. (12k+20k):(15k-8k) = 32k:7k = 32:7.

Q14.

A bag contains coins in the ratio 2:3:5. If there are 50 coins in all, find the number of each type.

A12, 18, 20

B8, 12, 30

C10, 15, 25

D15, 20, 15

Show Answer & Explanation

Correct Answer: C - 10, 15, 25

Total parts = 10. Each part = 5 coins. Coins: 10, 15, 25.

Q15.

The third proportional to 4 and 8 is:

A12

B16

C14

D20

Show Answer & Explanation

Correct Answer: B - 16

If 4:8::8:x, then 4x = 64. x = 16.

Q16.

Gold and copper are mixed in ratio 7:2. If 9 grams of mixture contains gold worth ₹315, find rate of gold per gram.

A₹45

B₹40

C₹50

D₹55

Show Answer & Explanation

Correct Answer: A - ₹45

Gold in 9g = 9×7/9 = 7g. Rate = 315/7 = ₹45 per gram.

Q17.

The ratio of ages of A and B is 4:3. After 6 years, ratio becomes 5:4. Find present ages.

A20 and 15

B24 and 18

C16 and 12

D28 and 21

Show Answer & Explanation

Correct Answer: B - 24 and 18

Let ages = 4x, 3x. (4x+6)/(3x+6) = 5/4. 16x+24 = 15x+30. x=6. Ages: 24, 18.

Q18.

A and B invest in ratio 3:2. A invests for 8 months, B for 12 months. Profit ratio is:

A1:2

B2:1

C1:1

D3:2

Show Answer & Explanation

Correct Answer: C - 1:1

Profit ratio = (3×8):(2×12) = 24:24 = 1:1.

Q19.

A mixture contains alcohol and water in ratio 4:3. If 10 liters of water is added, ratio becomes 4:5. Find original quantity.

A14 liters

B35 liters

C28 liters

D21 liters

Show Answer & Explanation

Correct Answer: B - 35 liters

Let mixture = 7x. Alcohol = 4x, Water = 3x. 4x/(3x+10) = 4/5. 20x = 12x+40. x=5. Total = 35.

Q20.

If A:B = 1:2, B:C = 3:4, C:D = 5:6, find A:D.

A5:16

B1:6

C3:8

D5:24

Show Answer & Explanation

Correct Answer: A - 5:16

A/D = (A/B)×(B/C)×(C/D) = (1/2)×(3/4)×(5/6) = 15/48 = 5/16. A:D = 5:16.

Q21.

If A:B = 2:3 and B:C = 4:5, then A:B:C is:

A2:3:5

B6:9:10

C4:6:9

D8:12:15

Show Answer & Explanation

Correct Answer: D - 8:12:15

Make B common: A:B = 8:12, B:C = 12:15. So A:B:C = 8:12:15.

Q22.

Divide ₹1200 among A, B, C in the ratio 2:3:5. C's share is:

A₹600

B₹500

C₹360

D₹480

Show Answer & Explanation

Correct Answer: A - ₹600

C's share = (5/10) × 1200 = 600.

Q23.

The ratio of boys to girls in a class is 3:2. If there are 30 boys, total students are:

A55

B45

C50

D40

Show Answer & Explanation

Correct Answer: C - 50

Boys=3x=30, x=10. Girls=2x=20. Total=50.

Q24.

If x:y = 3:4, then (2x+3y):(3x+4y) is:

A3:4

B15:20

C9:13

D18:25

Show Answer & Explanation

Correct Answer: D - 18:25

Let x=3k, y=4k. (6k+12k):(9k+16k) = 18k:25k = 18:25.

Q25.

Two numbers are in ratio 5:8. If 4 is subtracted from each, the ratio becomes 1:2. The numbers are:

A20 and 32

B10 and 16

C15 and 24

D25 and 40

Show Answer & Explanation

Correct Answer: B - 10 and 16

Let the numbers be 5x and 8x. Then (5x-4)/(8x-4)=1/2, so 10x-8=8x-4, giving x=2. The numbers are 10 and 16.

Q26.

If A:B = 1:2, B:C = 3:4, C:D = 5:6, then A:D is:

A1:4

B3:8

C5:16

D5:24

Show Answer & Explanation

Correct Answer: C - 5:16

A:B=1:2, B:C=3:4→A:B:C=3:6:8, C:D=5:6→A:B:C:D=15:30:40:48. A:D=15:48=5:16.

Q27.

A mixture has milk and water in ratio 4:1. If 5 litres of water is added, ratio becomes 4:3. How much milk is in the mixture?

A12 litres

B8 litres

C10 litres

D15 litres

Show Answer & Explanation

Correct Answer: C - 10 litres

Milk=4x, Water=x. 4x/(x+5)=4/3. 12x=4x+20. 8x=20. x=2.5. Milk=10.

Q28.

Three friends share profit in ratio 3:4:5. If total profit is ₹6000, middle friend's share is:

A₹2000

B₹1500

C₹2500

D₹1800

Show Answer & Explanation

Correct Answer: A - ₹2000

Middle (4) share = (4/12)×6000 = 2000.

Q29.

The mean proportional between 9 and 16 is:

A12.5

B12

C13

D11

Show Answer & Explanation

Correct Answer: B - 12

Mean proportional = √(9×16) = √144 = 12.

Q30.

If 2A = 3B = 4C, then A:B:C is:

A2:3:4

B6:4:3

C4:3:2

D3:2:1

Show Answer & Explanation

Correct Answer: B - 6:4:3

2A=3B=4C=k. A=k/2, B=k/3, C=k/4. A:B:C = 1/2:1/3:1/4 = 6:4:3.

Q31.

The fourth proportional to 4, 6, and 8 is:

A16

B10

C12

D14

Show Answer & Explanation

Correct Answer: C - 12

4:6 = 8:x. x = 6×8/4 = 12.

Q32.

Ages of A and B are in ratio 3:5. After 6 years, ratio will be 2:3. Present ages are:

A18 and 30

B12 and 20

C15 and 25

D9 and 15

Show Answer & Explanation

Correct Answer: A - 18 and 30

(3x+6)/(5x+6)=2/3. 9x+18=10x+12. x=6. Ages: 18 and 30.

Q33.

If a:b = 2:3, then (3a-2b):(2a+3b) is:

A0:13

B1:13

C-1:13

D2:13

Show Answer & Explanation

Correct Answer: A - 0:13

a=2k, b=3k. (6k-6k):(4k+9k) = 0:13k = 0:13.

Q34.

Rs.2850 is divided among P, Q, R such that P:Q = 5:3 and Q:R = 2:1. P gets:

ARs.1500

BRs.1800

CRs.1200

DRs.2000

Show Answer & Explanation

Correct Answer: A - Rs.1500

Make Q common: P:Q = 10:6 and Q:R = 6:3, so P:Q:R = 10:6:3. Total parts = 19. P gets 10/19 x 2850 = Rs.1500.

Q35.

Gold and copper are mixed in ratio 7:2. If 63g of gold is in the mixture, total weight is:

A81g

B72g

C90g

D99g

Show Answer & Explanation

Correct Answer: A - 81g

Gold=7x=63, x=9. Total=9x=81g.

Q36.

If the ratio of two numbers is 3:5 and their sum is 56, find the larger number.

A28

B30

C40

D35

Show Answer & Explanation

Correct Answer: D - 35

3x+5x=56. 8x=56. x=7. Larger=5×7=35.

Q37.

In a school, ratio of boys to girls is 7:5. If 120 more boys join, ratio becomes 9:5. How many girls are there?

A350

B250

C300

D200

Show Answer & Explanation

Correct Answer: C - 300

(7x+120)/5x=9/5. 35x+600=45x. 10x=600. x=60. Girls=300.

Q38.

A:B = 2:3, B:C = 5:7. Find A:C.

A14:15

B2:7

C5:7

D10:21

Show Answer & Explanation

Correct Answer: D - 10:21

A/B=2/3, B/C=5/7. A/C = (2/3)×(5/7) = 10/21.

Q39.

The salary of A, B, C are in ratio 2:3:5. If the total salary is ₹50000, A's salary is:

A₹12000

B₹15000

C₹25000

D₹10000

Show Answer & Explanation

Correct Answer: D - ₹10000

A = (2/10)×50000 = 10000.

Q40.

If the ratio 2a:3b equals 5:9, then a:b is:

A5:6

B6:5

C3:5

D5:3

Show Answer & Explanation

Correct Answer: A - 5:6

2a/3b=5/9. a/b = (5×3)/(9×2) = 15/18 = 5/6.

Q41.

Two alloys contain copper and tin in ratios 3:1 and 1:3. What ratio should they be mixed to get 1:1 alloy?

A1:2

B2:3

C3:2

D1:1

Show Answer & Explanation

Correct Answer: D - 1:1

Alloy1: 3/4 copper. Alloy2: 1/4 copper. Target: 1/2. By alligation: (1/2-1/4)/(3/4-1/2)=1/4÷1/4=1:1.

Q42.

A bag contains Rs.1, Rs.2, and Rs.5 coins in ratio 3:5:7. If total coins are 150, total amount is:

ARs.480

BRs.350

CRs.410

DRs.370

Show Answer & Explanation

Correct Answer: A - Rs.480

The ratio total is 15, so the multiplier is 10. Coins are 30 of Rs.1, 50 of Rs.2, and 70 of Rs.5. Total value = 30 + 100 + 350 = Rs.480.

Q43.

If p:q = 3:4 and q:r = 8:9, find p:q:r.

A6:4:9

B3:4:9

C3:8:9

D6:8:9

Show Answer & Explanation

Correct Answer: D - 6:8:9

Make q common: p:q=6:8, q:r=8:9. p:q:r=6:8:9.

Q44.

Income of A and B are in ratio 5:4 and expenses in ratio 3:2. Each saves Rs.2000. Income of A is:

ARs.10000

BRs.8000

CRs.12000

DRs.5000

Show Answer & Explanation

Correct Answer: D - Rs.5000

Let incomes be 5x and 4x, expenses be 3y and 2y. Since both save 2000: 5x-3y=2000 and 4x-2y=2000. Solving gives x=1000, so A's income is Rs.5000.

Q45.

The ratio of copper to zinc in an alloy is 5:3. If 16 kg of alloy is melted, copper in it is:

A10 kg

B8 kg

C12 kg

D6 kg

Show Answer & Explanation

Correct Answer: A - 10 kg

Copper = (5/8)×16 = 10 kg.

Q46.

If 3:x = x:12, then x equals:

A8

B4

C6

D9

Show Answer & Explanation

Correct Answer: C - 6

x² = 36. x = 6.

Q47.

The ratio of present ages of father and son is 7:2. After 5 years it will be 8:3. Father's present age is:

A28

B42

C35

D49

Show Answer & Explanation

Correct Answer: C - 35

(7x+5)/(2x+5)=8/3. 21x+15=16x+40. 5x=25. x=5. Father=35.

Q48.

Divide 147 into three parts such that they are in continued proportion and first part is 7. Second part is:

A28

B35

C14

D21

Show Answer & Explanation

Correct Answer: A - 28

In continued proportion, a:b = b:c, so b² = ac. With a=7 and b=28, c = 28²/7 = 112. The three parts are 7, 28, and 112, and their sum is 147.

Q49.

A:B:C = 2:3:4. If A's share of ₹900 is ₹200, find C's share.

A₹350

B₹400

C₹300

D₹450

Show Answer & Explanation

Correct Answer: B - ₹400

A=2x=200, x=100. C=4x=400.

Q50.

If a/b = c/d = e/f = 2/3, then (a+c+e)/(b+d+f) equals:

A2/3

BAll of these

C4/6

D6/9

Show Answer & Explanation

Correct Answer: B - All of these

By property of equal ratios, (a+c+e)/(b+d+f) = 2/3. 6/9 = 4/6 = 2/3. All same.

Q51.

If a:b = 3:5 and b:c = 10:7, then a:c is:

A3:7

B6:7

C7:6

D5:7

Show Answer & Explanation

Correct Answer: B - 6:7

Make b common: a:b=6:10 and b:c=10:7, so a:c=6:7.

Q52.

The ratio of two numbers is 7:11 and their difference is 48. The larger number is:

A84

B112

C132

D144

Show Answer & Explanation

Correct Answer: C - 132

Difference = 4 parts = 48, so 1 part = 12. Larger = 11 x 12 = 132.

Q53.

If 4x = 5y = 10z, then x:y:z is:

A5:4:2

B10:8:4

C2:4:5

D5:2:4

Show Answer & Explanation

Correct Answer: A - 5:4:2

Let common value be k. x=k/4, y=k/5, z=k/10. Ratio = 1/4:1/5:1/10 = 5:4:2.

Q54.

A sum is divided among A, B, C in ratio 2:3:5. If C gets Rs. 450 more than A, total sum is:

ARs. 1200

BRs. 1350

CRs. 1500

DRs. 1650

Show Answer & Explanation

Correct Answer: C - Rs. 1500

Difference between C and A is 3 parts = 450, so 1 part = 150. Total 10 parts = 1500.

Q55.

If x:y = 4:9, then sqrt(x):sqrt(y) is:

A2:3

B4:9

C16:81

D3:2

Show Answer & Explanation

Correct Answer: A - 2:3

Square root of 4:9 gives 2:3.

Q56.

Two numbers are in ratio 5:8. If 6 is added to each, ratio becomes 2:3. Smaller number is:

A30

B36

C42

D48

Show Answer & Explanation

Correct Answer: A - 30

(5k+6)/(8k+6)=2/3 gives 15k+18=16k+12, so k=6. Smaller=30.

Q57.

A mixture has milk and water in ratio 7:3. How much water must be added to 40 L mixture to make ratio 7:5?

A6 L

B8 L

C10 L

D12 L

Show Answer & Explanation

Correct Answer: B - 8 L

Milk=28 L, water=12 L. For 7:5, water should be 20 L. Add 8 L.

Q58.

If a:b:c = 2:3:4 and a+b+c = 81, then c-b is:

A6

B9

C12

D18

Show Answer & Explanation

Correct Answer: B - 9

Total parts=9, one part=9. c-b=(4-3) parts=9.

Q59.

The fourth proportional to 6, 9, and 14 is:

A18

B21

C24

D27

Show Answer & Explanation

Correct Answer: B - 21

If 6:9 = 14:x, then x = 9 x 14 / 6 = 21.

Q60.

A and B invest in ratio 5:7. A stays for 12 months, B for 8 months. Profit ratio is:

A15:14

B5:7

C3:2

D7:5

Show Answer & Explanation

Correct Answer: A - 15:14

Profit ratio = capital x time = 5x12 : 7x8 = 60:56 = 15:14.

Ratio & Proportion - Practice MCQs for CCAT

Ratio & Proportion Question Bank for C-CAT

Ratio & Proportion - Practice MCQs for CCAT

Ratio & Proportion Question Bank for C-CAT

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