50 Most Expected Ratio & Proportion Questions for AFCAT 2026 with Answers & Shortcut Tricks

Ratio & Proportion Questions for AFCAT 2026

50 Most Expected Questions with Shortcut Tricks

Important Formulas

Ratio: If A : B = 3 : 5. Then, A = 3x & B = 5x
Proportion: If A : B = C : D. Then, A × D = B × C

Question 1: The ratio of boys to girls in a class is 3 : 5. If there are 40 students, how many are boys?

A. 12
B. 15
C. 18
D. 20

Correct Answer - B. 15

Solution

Total Parts: 3+5=8
One Part: 40÷8=5
Boys - 3×5 =15

Shortcut

Total ÷ Sum of Ratio Parts
Then multiply with required ratio.

Question 2: The ratio of two numbers is 7 : 9. If their sum is 80, find the larger number.

A. 42
B. 45
C. 48
D. 50

Correct Answer - B. 45

Solution

Total Parts: 7+9=16
One Part: 80÷16=5
Larger Number: 9×5 =45

Question 3 : The ratio of Ravi's and Mohit's ages is 4 : 7. If Ravi is 16 years old, find Mohit's age.

A. 24
B. 26
C. 28
D. 30

Correct Answer - C. 28

Solution

4 Parts =16
1 Part =4
Mohit: 7×4 =28 years

Question 4: Two numbers are in the ratio 5 : 8. If the smaller number is 30, find the larger number.

A. 42
B. 45
C. 48
D. 50

Correct Answer - C. 48

Solution

5 Parts =30
1 Part =6
Larger Number: 8×6 =48

Question 5: The ratio of milk and water is 7 : 3. If there are 21 litres of milk, how much water is present?

A. 7 litres
B. 8 litres
C. 9 litres
D. 10 litres

Correct Answer - C. 9 litres

Solution

7 Parts =21
1 Part =3
Water: 3×3 =9 litres

Question 6: A bag contains red and blue balls in the ratio 5 : 7. If there are 84 balls, find the number of blue balls.

A. 35
B. 42
C. 49
D. 56

Correct Answer - C. 49

Solution

Total Parts: 5+7=12
One Part: 84÷12=7
Blue Balls: 7×7 =49

Question 7: The ratio of income to expenditure is 7 : 5. If income is ₹42,000, find expenditure.

A. ₹28,000
B. ₹30,000
C. ₹32,000
D. ₹35,000

Correct Answer - B. ₹30,000

Solution

7 Parts =42,000
1 Part =6,000
Expenditure- 5×6,000 =₹30,000

Question 8: If A : B = 2 : 3 and B : C = 4 : 5. Find A : B : C

A. 8 : 12 : 15
B. 6 : 9 : 10
C. 4 : 6 : 8
D. 10 : 15 : 20

Correct Answer: A. 8 : 12 : 15

Question 9: If 3 : x = 9 : 15. Find x.

A. 4
B. 5
C. 6
D. 7

Correct Answer - B. 5

Solution

3/x =9/15 Cross Multiply 45=9x
x=5

Question 10: The ratio of two numbers is 9 : 11. Their difference is 20. Find the larger number.

A. 100
B. 110
C. 120
D. 130

Correct Answer - B. 110

Solution

Difference in ratio: 11−9=2
2 Parts =20
1 Part =10
Larger Number: 11×10 =110

Question 11: A and B invest money in the ratio 5 : 8. After one year, they earn a profit of ₹52,000. Find B's share.

A. ₹30,000
B. ₹32,000
C. ₹34,000
D. ₹36,000

Correct Answer - B. ₹32,000

Solution

Total ratio = 5 + 8 = 13
B's Share = (8/13) × 52,000 = ₹32,000

Question 12: The ratio of Amit's Income : Expenditure is 7 : 5. If his monthly savings are ₹12,000, find his monthly income.

A. ₹36,000
B. ₹40,000
C. ₹42,000
D. ₹48,000

Correct Answer - C. ₹42,000

Solution

Savings = Income − Expenditure
Ratio Difference = 7 − 5 = 2
2 Parts = ₹12,000
1 Part = ₹6,000
Income = 7 × ₹6,000 = ₹42,000

Question 13: A : B = 3 : 5, B : C = 10 : 7. Find A : B : C.

A. 6 : 10 : 7
B. 3 : 10 : 7
C. 9 : 15 : 14
D. 12 : 20 : 14

Correct Answer - A. 6 : 10 : 7

Question 14: Milk and water are mixed in the ratio 7 : 3. How much water should be added to 40 litres of the mixture to make the ratio 7 : 5?

A. 6 litres
B. 8 litres
C. 10 litres
D. 12 litres

Correct Answer - B. 8 litres

Solution

In 40 litres: Milk = (7/10) × 40 = 28 L & Water = (3/10) × 40 = 12 L
Let x litres of water be added. 28 : (12 + x) = 7 : 5
Cross multiply: 140 = 84 + 7x, 56 = 7x
x = 8 litres

Question 15 : The present ages of A and B are in the ratio 4 : 5. After 8 years, their ages become 12 : 14. Find A's present age.

A. 24 years
B. 28 years
C. 16 years
D. 36 years

Correct Answer - C. 16 years

Solution

Let present ages be: 4x and 5x
After 8 years: (4x + 8) / (5x + 8) = 12 / 14 = 6 / 7
7(4x + 8) = 6(5x + 8)
28x + 56 = 30x + 48
2x = 8
x = 4

Present age of A = 4x = 16 years

Question 16: If 15 workers complete a job in 24 days, how many workers are required to complete it in 18 days?

A. 18
B. 20
C. 22
D. 24

Correct Answer: B. 20

Solution

Workers × Days = Constant
15 × 24 = W × 18
W = 360 ÷ 18 = 20 workers

Question 17: The ratio of two numbers is 11 : 15. Their difference is 48. Find the larger number.

A. 160
B. 180
C. 192
D. 200

Correct Answer - B. 180

Solution

Difference in ratio = 15 − 11 = 4
4 Parts = 48
1 Part = 12
Larger Number = 15 × 12 = 180

Question 18: If x : y = 5 : 8 and y : z = 12 : 7. Find x : y : z.

A. 15 : 24 : 14
B. 10 : 16 : 14
C. 20 : 32 : 21
D. 25 : 40 : 21

Correct Answer - A. 15 : 24 : 14

Question 19: A prize money of ₹76,500 is divided among A, B and C in the ratio 4 : 5 : 8. Find C's share.

A. ₹30,000
B. ₹32,000
C. ₹36,000
D. ₹36,000

Correct Answer - C. ₹36,000

Solution

Total Ratio = 4 + 5 + 8 = 17
One Part = ₹76,500 ÷ 17 = ₹4,500
C's Share = 8 × ₹4,500 = ₹36,000

Question 20: The ratio of two numbers is 7 : 9. If 20% of the first number equals 14% of the second number, find the numbers.

A. 35 and 45
B. 70 and 90
C. No such pair exists
D. 140 and 180

Correct Answer - C. No such pair exists

Solution

If the numbers are in the ratio 7 : 9,
let them be 7x and 9x.
Given: 20% of first = 14% of second 0.20 × 7x = 0.14 × 9x
1.4x = 1.26x This implies: 1.4 ≠ 1.26
The condition is impossible.

Hence, no such pair exists.

Question 21: A invests ₹40,000 for 12 months and B invests ₹60,000 for 8 months. If the total profit is ₹48,000, find B's share.

A. ₹22,000
B. ₹24,000
C. ₹26,000
D. ₹28,000

Correct Answer - B. ₹24,000

Solution

Profit Ratio = Investment × Time
A = 40,000 × 12 = 4,80,000
B = 60,000 × 8 = 4,80,000
Ratio = 1 : 1

B's Share = ₹48,000 ÷ 2 = ₹24,000

Question 22: Five years ago, the ages of A and B were in the ratio 3 : 4. After 10 years, the ratio becomes 5 : 6. Find A's present age.

A. 20 years
B. 27.5 years
C. 30 years
D. 35 years

Correct Answer - B. 27.5 years

Solution

Let ages 5 years ago be: 3x and 4x
After 15 years: (3x + 15) / (4x + 15) = 5 / 6
6(3x + 15) = 5(4x + 15)
18x + 90 = 20x + 75
2x = 15
x = 7.5
Present age of A = 3x + 5 = 22.5 + 5 = 27.5 years

Question 23: A container has 60 litres of milk. 15 litres are removed and replaced with water. The process is repeated once again. Find the quantity of milk left.

A. 33.75 L
B. 37.50 L
C. 40.00 L
D. 42.19 L

Correct Answer - A. 33.75 L

Solution

Milk Remaining = Initial Milk × (1 − Removed/Total)² = 60 × (45/60)² = 60 × (3/4)² = 60 × 9/16 = 33.75 litres

Question 24: A : B = 2 : 5, B : C = 3 : 4, C : D = 8 : 7. Find A : B : C : D.

A. 6 : 15 : 20 : 17.5
B. 12 : 30 : 40 : 35
C. 18 : 45 : 60 : 52
D. 24 : 60 : 80 : 70

Correct Answer - B. 12 : 30 : 40 : 35

Question 25: Income : Expenditure = 9 : 7, Savings = ₹16,000. Find Income.

A. ₹64,000
B. ₹72,000
C. ₹80,000
D. ₹88,000

Correct Answer - B. ₹72,000

Question 26: If 18 workers complete a work in 20 days, how many workers are required to complete the same work in 15 days?

A. 22
B. 24
C. 26
D. 28

Correct Answer - B. 24

Solution

Workers × Days = Constant
18 × 20 = W × 15
W = 24 workers

Question 27: The ratio of two numbers is 11 : 14 and their sum is 200. Find the smaller number.

A. 80
B. 88
C. 96
D. 104

Correct Answer - B. 88

Solution

Total Parts = 25
One Part = 200 ÷ 25 = 8
Smaller Number = 11 × 8 = 88

Question 28: The ratio of A : B = 4 : 5, B : C = 6 : 7, C : D = 8 : 9. Find A : B : C : D.

A. 96 : 120 : 140 : 157.5
B. 96 : 120 : 140 : 157
C. 96 : 120 : 140 : 158
D. None of these

Correct Answer - D. None of these

Solution

LCM method gives: A : B : C : D = 96 : 120 : 140 : 157.5
Since ratios are normally expressed as whole numbers,
Multiply all terms by 2: = 192 : 240 : 280 : 315
This option is not given.
Hence, None of these.

Question 29: If x : 12 = 15 : 20. Find x.

A. 8
B. 9
C. 10
D. 11

Correct Answer - B. 9

Solution

x/12 = 15/20
x = (12 × 15) ÷ 20 = 9

Question 30: The ratio of the present ages of A and B is 5 : 7. Eight years ago, their ages were in the ratio 3 : 5. Find B's present age.

A. 28 years
B. 35 years
C. 42 years
D. 56 years

Correct Answer - A. 28 years

Solution

Let present ages be: 5x and 7x
Eight years ago: (5x − 8) / (7x − 8) = 3 / 5
5(5x − 8) = 3(7x − 8)
25x − 40 = 21x − 24
4x = 16
x = 4
Present age of B = 7 × 4 = 28 years

Question 31 :A invests ₹60,000 for 12 months while B invests ₹80,000 for 9 months. If the total profit is ₹69,000, find B's share.

A. ₹33,000
B. ₹34,500
C. ₹36,000
D. ₹39,000

Correct Answer - B. ₹34,500

Solution

Investment × Time
A = 60,000 × 12 = 7,20,000
B = 80,000 × 9 = 7,20,000
Profit Ratio = 1 : 1
B's Share = 69,000 ÷ 2 = ₹34,500

Question 32: A : B = 4 : 7, B : C = 3 : 5, C : D = 10 : 9. Find A : B : C : D.

A. 24 : 42 : 70 : 63
B. 12 : 21 : 35 : 30
C. 8 : 14 : 20 : 18
D. 16 : 28 : 40 : 36

Correct Answer - A. 24 : 42 : 70 : 63

Solution

Equalize B and C:
4 : 7 → ×6 = 24 : 42
3 : 5 → ×14 = 42 : 70
10 : 9 → ×7 = 70 : 63
Final Ratio = 24 : 42 : 70 : 63

Question 33: The present ages of A and B are in the ratio 5 : 8. After 9 years, the ratio becomes 7 : 10. Find A's present age.

A. 30 years
B. 22.5 years
C. 40 years
D. 45 years

Correct Answer - B. 22.5 years

Solution

Let present ages = 5x and 8x
After 9 years: (5x + 9)/(8x + 9) = 7/10
50x + 90 = 56x + 63
6x = 27
x = 4.5

Present age of A = 5x = 22.5 years

Question 34: A mixture contains milk and water in the ratio 9 : 4. If 13 litres of water are added, the ratio becomes 9 : 5. Find the original quantity of the mixture.

A. 104 litres
B. 169 litres
C. 130 litres
D. 143 litres

Correct Answer - B. 169 litres

Solution

Let original mixture = 13x
Milk = 9x
Water = 4x
After adding 13 litres:
9x : (4x + 13) = 9 : 5
45x = 36x + 117
9x = 117
x = 13

Original mixture = 13 × 13 = 169 litres

Question 35: ₹1,08,000 is divided among A, B and C in the ratio 3 : 4 : 5. Find the difference between the shares of C and A.

A. ₹15,000
B. ₹18,000
C. ₹20,000
D. ₹22,000

Correct Answer - B. ₹18,000

Solution

Total Parts = 12
One Part = 1,08,000 ÷ 12 = ₹9,000
Difference = (5 − 3) × ₹9,000 = ₹18,000

Question 36: If x : 18 = 20 : 30. Find x.

A. 10
B. 11
C. 12
D. 13

Correct Answer - C. 12

Solution

x/18 = 20/30
x = (18 × 20)/30 = 12

Question 37: The ratio of two numbers is 13 : 17. Their difference is 72. Find the larger number.

A. 288
B. 306
C. 324
D. 340

Correct Answer - B. 306

Solution

Difference in ratio = 4
One part = 72 ÷ 4 = 18
Larger number = 17 × 18 = 306

Question 38: Income : Expenditure = 11 : 8. If savings are ₹15,000, find the expenditure.

A. ₹35,000
B. ₹40,000
C. ₹44,000
D. ₹48,000

Correct Answer - B. ₹40,000

Solution

Difference = 3 parts
3 Parts = ₹15,000
1 Part = ₹5,000
Expenditure = 8 × ₹5,000 = ₹40,000

Question 39: A : B = 2 : 3, B : C = 4 : 5, C : D = 6 : 7. Find A : B : C : D.

A. 16 : 24 : 30 : 35
B. 8 : 12 : 15 : 17.5
C. 24 : 36 : 45 : 52.5
D. None of these

Correct Answer: A. 16 : 24 : 30 : 35

Solution

Equalize B and C:
2 : 3 → ×8 = 16 : 24
4 : 5 → ×6 = 24 : 30
6 : 7 → ×5 = 30 : 35

Final Ratio = 16 : 24 : 30 : 35

Question 40: The ratio of two numbers is 7 : 11. If 15 is added to both numbers, the ratio becomes 4 : 6. Find the smaller number.

A. 30
B. 105
C. 42
D. 49

Correct Answer - B. 105

Solution

Let the numbers be 7x and 11x.
After adding 15: (7x + 15) / (11x + 15) = 4 / 6 = 2 / 3
3(7x + 15) = 2(11x + 15)
21x + 45 = 22x + 30
x = 15
Smaller number = 7 × 15 = 105

Question 41: A invests ₹50,000 for 12 months and B invests ₹80,000 for 9 months. The total profit is ₹1,02,000. Find B's share.

A. ₹55,636
B. ₹52,000
C. ₹54,000
D. ₹56,000

Correct Answer - A. ₹55,636

Solution

Investment × Time
A = 50,000 × 12 = 6,00,000
B = 80,000 × 9 = 7,20,000
Ratio = 5 : 6
B's Share = (6/11) × 1,02,000 = ₹55,636.36

Question 42: The present ages of A and B are in the ratio 7 : 9. After 8 years, their ages become 5 : 6. Find A's present age.

A. 18 years
B. 35 years
C. 42 years
D. 49 years

Correct Answer - A. 18 years

Solution

Let present ages be 7x and 9x.
(7x + 8)/(9x + 8) = 5/6
42x + 48 = 45x + 40
3x = 8
x = 8/3
Present age = 56/3 = 18⅔ years

Question 43: Milk and water are mixed in the ratio 5 : 3. If 16 litres of water are added, the ratio becomes 5 : 5. Find the original quantity of the mixture.

A. 64 litres
B. 80 litres
C. 96 litres
D. 128 litres

Correct Answer - A. 64 litres

Solution

Let the original mixture be 8x litres.
Milk = 5x
Water = 3x
After adding 16 litres:
5x : (3x + 16) = 1 : 1
5x = 3x + 16
2x = 16
x = 8

Original mixture = 8 × 8 = 64 litres

Question 44: ₹1,44,000 is divided among A, B and C in the ratio 5 : 7 : 6. Find B's share.

A. ₹48,000
B. ₹54,000
C. ₹56,000
D. ₹60,000

Correct Answer - C. ₹56,000

Solution

Total Parts = 18
One Part = 1,44,000 ÷ 18 = ₹8,000
B's Share = 7 × 8,000 = ₹56,000

Question 45: The ratio of two numbers is 8 : 13. Their difference is 45. Find the larger number.

A. 104
B. 117
C. 120
D. 135

Correct Answer - B. 117

Solution

Difference in ratio = 5
One Part = 45 ÷ 5 = 9
Larger Number = 13 × 9 = 117

Question 46: A : B = 4 : 7, B : C = 6 : 5. Find A : B : C.

A. 24 : 42 : 35
B. 12 : 21 : 15
C. 8 : 14 : 10
D. 16 : 28 : 20

Correct Answer: A. 24 : 42 : 35

Solution

Equalize B.

4 : 7 × 6 = 24 : 42
6 : 5 × 7 = 42 : 35

Final Ratio = 24 : 42 : 35

Question 47: Income : Expenditure = 13 : 9. If monthly savings are ₹20,000, find the monthly income.

A. ₹60,000
B. ₹65,000
C. ₹70,000
D. ₹72,000

Correct Answer - B. ₹65,000

Solution

Difference = 4 Parts
4 Parts = ₹20,000
1 Part = ₹5,000
Income = 13 × 5,000 = ₹65,000

Question 48: If x : 15 = 18 : 30. Find x.

A. 8
B. 9
C. 10
D. 11

Correct Answer - B. 9

Solution

x/15 = 18/30
x = (15 × 18) ÷ 30 = 9

Question 49: If 24 workers complete a work in 15 days, how many workers are needed to complete the same work in 10 days?

A. 30
B. 32
C. 36
D. 40

Correct Answer - C. 36

Solution

Workers × Days = Constant
24 × 15 = W × 10
W = 36

Question 50: The ratio of two numbers is 9 : 14. If 25 is added to each number, the ratio becomes 2 : 3. Find the smaller number.

A. 135
B. 180
C. 225
D. 270

Correct Answer - A. 225

Solution

Let numbers be 9x and 14x.
(9x + 25)/(14x + 25) = 2/3
3(9x + 25) = 2(14x + 25)
27x + 75 = 28x + 50
x = 25
Smaller number = 9 × 25 = 225

Final Formula Sheet

Ratio: If A : B = m : n
Then, A = mx & B = nx

Proportion: A : B = C : D ⇒ A × D = B × C

Partnership =Profit ∝ Investment × Time

Workers =Workers × Days = Constant

Distribution =One Part = Total ÷ Sum of Ratio Parts

Savings =Savings = Income − Expenditure

Last-Minute AFCAT Tips

Always simplify ratios before solving.
Use the LCM method for combined ratios.
In partnership questions, multiply Investment × Time.
In age questions, form equations instead of guessing.
Check whether the options match your calculated answer.

Practice Challenge

A : B = 5 : 8, B : C = 4 : 7. Find A : B : C.
₹96,000 is divided in the ratio 3 : 5 : 8. Find the largest share.
The ratio of two numbers is 7 : 12 and their sum is 190. Find both numbers.
Income : Expenditure = 8 : 5. Savings = ₹18,000. Find Income.
A invests ₹80,000 for 9 months and B invests ₹60,000 for 12 months. Profit = ₹90,000. Find each partner's share.

Conclusion

Ratio & Proportion is one of the highest-scoring topics in AFCAT. Most questions become straightforward if you remember a few standard methods:

Find one part first.
Use LCM for combined ratios.
Multiply Investment × Time in partnership.
Use equations for age problems.
Verify calculations before selecting an option.

By mastering these 50 questions and revising the formulas regularly, you can solve most Ratio & Proportion questions quickly and accurately in the AFCAT exam.