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

An amount is distributed among X, Y and Z in the ratio of 3 : 5 : 7 and another amount is equally distributed between P and Q. If the difference between the amount of Y and Q is Rs. 3500, how much amount will P get?

  1. Rs. 150

  2. Rs. 300

  3. Rs. 650

  4. Data inadequate

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

The question provides two separate distribution scenarios but only gives the difference between Y and Q amounts. We cannot determine either total amount since we have only one equation with multiple unknowns. The ratio gives Y = 5x, and equal distribution gives Q = y/2, but knowing Y - Q = 3500 doesn't let us solve for x or y individually. Therefore, data is inadequate to find P's share.

Multiple choice

Three numbers are in the ratio (1 : 3 : 4) and their sum is 96. The third number is half of the sum. Find the difference between the sum of the first two numbers and the third number?

  1. 2

  2. 0

  3. 3

  4. 9

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

If numbers are 1x, 3x, 4x then sum is 8x = 96, so x = 12. Third number = 4x = 48. First two sum = 1x + 3x = 48. Difference = 48 - 48 = 0. The statement 'third number is half of sum' is consistent with 48 = 96/2.

Multiple choice

A bag contains 50 paise, 25 paise and 10 paise coins are in the ratio of 5 : 9 : 4 respectively amounting to Rs. 206. Find the number of coins of 50 paise?
  1. $200$
  2. $235$
  3. $211$
  4. $225$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let coins be in ratio 5:9:4. Let actual counts be 5k, 9k, 4k. Total value = (5k × 0.50) + (9k × 0.25) + (4k × 0.10) = 2.5k + 2.25k + 0.4k = 5.15k = Rs. 206. So k = 206/5.15 = 40. Number of 50 paise coins = 5k = 5 × 40 = 200. Option A is correct.

Multiple choice

Weekly incomes of two persons are in the ratio of 7 : 3 and their weekly expenses are in the ratio of 5 : 2. If each of them saves Rs. 300 per week, then the weekly income of the first person is -

  1. Rs. 4660

  2. Rs. 4880

  3. Rs. 5600

  4. Rs. 6300
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Set incomes as 7x and 3x, expenses as 5y and 2y. Each person saves Rs. 300, so 7x - 5y = 300 and 3x - 2y = 300. Solving this system gives x = 900, so first person's income = 7 × 900 = Rs. 6300. The system of linear equations comes from income minus expense equals savings.

Multiple choice

An amount of money is to be divided among A, B and C in the ratio 5:11:23 respectively. If the difference between the total share of A and B together and C's share is Rs. 2800. What is the difference between B and C's share?

  1. Rs. 3680

  2. Rs. 4800

  3. Rs. 4600

  4. Rs. 5200
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let shares be 5k, 11k, 23k. Difference between A+B together and C is (5+11-23)k = -7k = 2800, so k = 400. Difference between B and C is (23-11)k = 12k = 12 × 400 = Rs. 4800. This tests ratio concepts and careful parsing of comparison language.

Multiple choice

The following questions are accompanied by three statement A, B and C. You have to determine which statement(s) is/are necessary/sufficient to answer the question. What is the monthly salary of Amit? (A) Amit's monthly salary is Rs. 3000 more than that of Billa. (B) The ratio of monthly salaries of Amit and Billa is 5 : 4 (C) The annual salary of Billa is Rs. 46800.

  1. Only A & B together.

  2. Only B & C are together

  3. All A, B & C are necessary

  4. Any two of them are sufficient

  5. A, B & C even together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

With A and B: A = B+3000 and A/B = 5/4 gives B=12000, A=15000. With B and C: A/B = 5/4 and B = 46800/12 = 3900 gives A = 4875. With A and C: A = B+3000 and B = 3900 gives A = 6900. Each pair of statements uniquely determines Amit's salary.

Multiple choice

A sum of Rs. 300 is divided among P, Q and R in such a way that Q gets Rs. 30 more than P and R gets Rs. 60 more than Q. The ratio of their shares is -
  1. $2:3:5$
  2. $3:2:5$
  3. $2:5:3$
  4. $5:3:2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let P's share = x. Then Q = x + 30, R = (x + 30) + 60 = x + 90. Total: x + (x + 30) + (x + 90) = 300, so 3x + 120 = 300, 3x = 180, x = 60. Shares are P = 60, Q = 90, R = 150. Ratio 60:90:150 = 2:3:5. Option A is correct. Option B reverses P and Q, Option C has wrong order, and Option D is completely reversed.

Multiple choice

Monthly incomes of two persons are in the ratio 5:4 and their expenditures are in the ratio 9:7. If each saves Rs. 500 per month, then what are their monthly income?

  1. Rs. 4500, Rs. 3600

  2. Rs. 4000, Rs. 2800

  3. Rs. 3500, Rs. 2800

  4. Rs. 5000, Rs. 4000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let incomes be 5x and 4x; expenditures be 9y and 7y. Savings = Income - Expenditure, so 5x - 9y = 500 and 4x - 7y = 500. Solving: Multiply second eq by 9: 36x - 63y = 4500. Multiply first by 7: 35x - 63y = 3500. Subtract: x = 1000. Therefore incomes are 5(1000) = 5000 and 4(1000) = 4000.

Multiple choice

A precious stone weighing 35 grams worth Rs. 12250 is accidentally dropped and gets broken into two pieces having weights in the ratio 2 : 5. If the price varies as the square of the weight then find the loss incurred.

  1. Rs. 4500

  2. Rs. 5000

  3. Rs. 5200

  4. Rs. 5700

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

Total weight = 35g in ratio 2:5. First piece = (2/7) × 35 = 10g, second piece = (5/7) × 35 = 25g. Price varies as square of weight, so price ∝ w². Original value ∝ 35² = 1225. New value ∝ 10² + 25² = 100 + 625 = 725. Loss in value ∝ 1225 - 725 = 500. Given 1225 corresponds to Rs. 12250, 500 corresponds to Rs. 5000. Option B is correct.

Multiple choice

The ratio of earning of Trishika and Yashika is 5 : 6. If the earnings of Trishika decreases by 25% and the earnings of Yashika increases by 20% the new ratio becomes 6 : 11. What is Yashika earnings per month?

  1. Rs. 25000

  2. Rs. 22000

  3. Can’t be determined

  4. Rs. 21000

  5. Rs. 24500
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Yashika's earnings cannot be determined from the given information. The ratios provide relationships but no absolute values. Initial ratio 5:6 and modified ratio 6:11 after percentage changes don't give a unique solution for actual earnings.