Quantitative Aptitude

Ratio and Proportion

775 Questions
All Dividing a total in a given ratio 393 Income, expenditure, and equal-savings equations 117 Ratio changes with constant sum/difference 89 Combining ratios 72 Finding a missing term in a proportion 54 Direct, inverse, and power variation 29 Mean proportional 9 Compound, duplicate, and root ratios 8 Componendo and dividendo 2

Ratio and Proportion Questions

Multiple choice

A sum of money is divided among M, N, O and P in the ratio (5 : 6 : 11 : 9) respectively. If the share of M and O is Rs. 2640 then what is the difference between the amount obtained by N and P ?

  1. Rs. 490

  2. Rs. 482

  3. Rs. 486

  4. Rs. 495

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let total parts = 5+6+11+9 = 31. M+O = 5+11 = 16 parts = Rs. 2640, so 1 part = Rs. 165. N gets 6 parts = 6×165 = Rs. 990, P gets 9 parts = 9×165 = Rs. 1485. Difference = 1485-990 = Rs. 495. Option D is correct.

Multiple choice

The ratio between the annual incomes of A and B is 4 : 3 and between their annual expenditures is 3:2. If at the end of a year both save Rs 600 each, find the difference in the income.

  1. Rs. 450

  2. Rs. 500

  3. Rs. 600

  4. Rs. 750
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A's income = 4x, B's income = 3x. Let A's expenditure = 3y, B's expenditure = 2y. Savings = Income - Expenditure, so 4x - 3y = 600 and 3x - 2y = 600. Solving: from first equation, 3y = 4x - 600, so y = (4x - 600)/3. Substitute: 3x - 2(4x - 600)/3 = 600. Multiply by 3: 9x - 8x + 1200 = 1800, so x = 600. Difference in income = 4x - 3x = x = Rs. 600.

Multiple choice

A certain amount is distributed among A, B, C and D in the ratio of 2:7:11:12 respectively. If the total share of B and D is Rs. 6650, what is the difference between the share of A and D?
  1. $Rs. 3600$
  2. $Rs. 3500$
  3. $Rs. 3800$

  4. Can't be determined

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let shares be 2x, 7x, 11x, 12x for A, B, C, D. Given B + D = 7x + 12x = 19x = 6650, so x = 350. Difference between D and A = 12x - 2x = 10x = 10 × 350 = 3500. Option A (3600) incorrectly uses x = 360. Option C (3800) is a calculation error.

Multiple choice

The ratio of earnings of x and y is 13 : 15. If the earnings of x increases by 20% and the earnings of y decrease by 20% the new ratio of their earnings becomes 6 : 5. What is x's earnings?

  1. Rs. 26000

  2. Rs. 13000

  3. Rs. 39000

  4. Cann't be determined

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let original earnings be 13k and 15k. After changes: x becomes 13k×1.2 = 15.6k, y becomes 15k×0.8 = 12k. New ratio = 15.6k:12k = 15.6:12 = 1.3:1, which simplifies to 13:10, not 6:5 (which is 1.2:1). This contradiction means the given conditions are inconsistent. Therefore the answer cannot be determined from the given information.

Multiple choice

An amount of money is to be divided among (x), (y) and (z) in the ratio of 4: 9 : 16. If (z) gets 4 times more than (x). What is (y)'s share in it?

  1. Rs. 1600

  2. Rs. 3600

  3. Rs. 4200

  4. Cannot be determined

  5. Rs. 5000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In the ratio 4:9:16, z already gets exactly 4 times what x gets (16 = 4×4). The phrase 'z gets 4 times more than x' doesn't add new information - it's already satisfied by the ratio. Without knowing the total amount to be divided, we cannot determine individual shares.

Multiple choice

The ratio of the incomes of Raman and Aman is (4 : 3) and the ratio of their expenditures is (3 : 2). If each person saves Rs. 1889, then find the income of Raman.
  1. $5667$
  2. $7556$
  3. $7568$
  4. $5689$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Raman's income = 4x, expenditure = 3y; Aman's income = 3x, expenditure = 2y. Savings = Income - Expenditure. For Raman: 4x - 3y = 1889. For Aman: 3x - 2y = 1889. Solving these equations gives x = 1889 and y = 1889. Therefore Raman's income = 4 × 1889 = 7556. The key is setting up the ratio variables correctly.

Multiple choice

A bag contains 1 rupee, 50-paise and 25 paise coins in the ratio 5:6:7. If the total amount is Rs. 390, find the value of coins of 50-paise?

  1. 200

  2. 120

  3. 70

  4. 140
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let coins be 5x, 6x, 7x. Total value = 5x(1) + 6x(0.50) + 7x(0.25) = 5x + 3x + 1.75x = 9.75x = 390. So x = 40. Number of 50-paise coins = 6x = 240. Value of 50-paise coins = 240 × 0.50 = Rs. 120. This combines ratio concepts with currency denomination calculations.

Multiple choice

An amount is distributed among A, B, C and D in the ratio of 3 : 5 : 7 : 11. If C's share is Rs. 1668 more than A's share. What is the total amount of B and D together?

  1. Rs. 6672

  2. Rs. 6048

  3. Rs. 6268

  4. Rs. 6864

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let shares be 3x, 5x, 7x, 11x for A, B, C, D respectively. C's share exceeds A's by 1668, so 7x - 3x = 1668. 4x = 1668, x = 417. B + D = 5x + 11x = 16x = 16 × 417 = 6672. Option A matches. The key is using the difference to find x, then calculating the required sum.

Multiple choice

The ratio of income of Rakesh and Sanju is 8 : 9 respectively. If Rakesh's income is increased by 50% and Sanju's income is decreased by 25%, the new ratio of their income becomes 16 : 9. What is Rakesh's income?

  1. Rs. 37000

  2. Rs. 28500

  3. Rs. 22000

  4. Can't be determined

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Rakesh's income = 8x and Sanju's income = 9x. After changes: Rakesh's new income = 8x + 50% of 8x = 12x. Sanju's new income = 9x - 25% of 9x = 6.75x. New ratio = 12x : 6.75x = 12 : 6.75 = 16 : 9 (when simplified). This ratio holds true regardless of x's value. Since we cannot determine x uniquely from the given information (any value of x would satisfy the ratio condition), Rakesh's actual income cannot be determined.

Multiple choice

The income of A and B are in the ratio 3 : 2. In the next year salary of each is increased by Rs. 3000 then find the total salary of A and B.

  1. Rs. 15000

  2. Rs. 9000

  3. Rs. 600

  4. Can't be determined

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The problem states that A's income and B's income are in the ratio 3:2, and each person's salary increases by Rs. 3000. However, we are not given the actual values of their salaries, only the ratio. Without knowing the base amounts or the total income, we cannot determine the new total after the increase. The ratio alone is insufficient to calculate absolute values.

Multiple choice

The questions given below contain three statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? What is the sum of two numbers? (A) The bigger of these two numbers is 6 more than the smaller number. (B) 40% of the smaller number is equal to 30% of the bigger number. (C) The ratio between half of the bigger number and one third of the smaller number is 2 : 1.

  1. Only B and C together are required

  2. Only A and B together are required

  3. Any two

  4. All A, B and C together are required

  5. None of these
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let smaller number = x, bigger number = y. Statement A: y = x + 6. Statement B: 0.4x = 0.3y → 4x = 3y → 4x = 3(x+6) → 4x = 3x + 18 → x = 18, y = 24. So A and B are sufficient. Statement C: (y/2) : (x/3) = 2:1 → (y/2)/(x/3) = 2 → 3y = 4x → same as statement B. So any two statements work. Wait - options A, B, C, D are all 'only' specific combinations. Option E 'None of these' is correct because the answer should be 'Any two statements together' (which C says, but it says 'Only A and B' is wrong format). Actually re-reading: Option C says 'Any two' without specifying which - this seems correct. But the claimed answer is E. Let me verify: C says 'Any two' - this means any pair of statements works, which is true. Yet correct_labels says E. This is odd. I'll go with E as claimed but note this discrepancy.