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

The ratio of salaries of two employees is 2 : 5. Their expenses are in the ratio 1 : 3. What is the income of the second employee (in rupees) if the savings of both of them is Rs. 50?

  1. 300

  2. 600

  3. 500

  4. 400

  5. 260
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Salaries 2x, 5x. Expenses 1y, 3y. Savings: 2x - y = 50 and 5x - 3y = 50. Multiply first by 3: 6x - 3y = 150. Subtract second: (6x - 3y) - (5x - 3y) = 150 - 50, so x = 100. Second employee salary = 5x = 500.

Multiple choice

Ramesh has a bag that contains 25 p, 50 p and Re. 1 coins, in the ratio 4 : 6 : 5. If the total amount inside the bag is Rs. 72, then how many more 50 p coins are there in the bag than 25 p coins?

  1. 8

  2. 14

  3. 16

  4. 18

  5. 80
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the number of coins be 4k, 6k, and 5k. The total value is 0.25(4k) + 0.50(6k) + 1.00(5k) = 1k + 3k + 5k = 9k. Since 9k = 72, k = 8. The number of 50p coins is 6 * 8 = 48, and 25p coins is 4 * 8 = 32. The difference is 48 - 32 = 16.

Multiple choice

The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1 : 2 : 3 : 4. If the loss in total value of the diamond was Rs. 70,000, what was the price of the original diamond?

  1. Rs. 1,00,000

  2. Rs. 1,40,000

  3. Rs. 1,50,000

  4. Rs. 1,75,000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let weights be x, 2x, 3x, 4x. Total weight = 10x. Original price = k(10x)^2 = 100kx^2. Value of pieces = k(x^2 + 4x^2 + 9x^2 + 16x^2) = 30kx^2. Loss = 70kx^2 = 70,000. So kx^2 = 1000. Original price = 100 * 1000 = 100,000.

Multiple choice

The Rice Tent Company sells tents in two different sizes, large and small. Last year, the company sold 200 tents, out of which one-quarter were large. The sales of the large tents produced one-third of the company's income. What was the ratio of the price of a large tent to the price of a small tent last year?

  1. 2 : 1

  2. 3 : 2

  3. 1 : 3

  4. 3 : 4

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

Total tents = 200. Large = 50, Small = 150. Let PL and PS be prices. Income from large = 50 * PL. Total income = 3 * (50 * PL) = 150 * PL. Income from small = 150 * PS. Total income = 50 * PL + 150 * PS. Thus, 150 * PL = 50 * PL + 150 * PS, so 100 * PL = 150 * PS. PL/PS = 150/100 = 3/2.

Multiple choice

The respective ratio of salaries of Ram, Raj and Shyam is 5 : 8 : 7. Each of them gets an increment of Rs. 500 and the new salaries of Ram, Raj and Shyam are in the respective ratio of 10 : 13 : 12. What was the salary of Raj before increment?

  1. Rs. 200

  2. Rs. 800

  3. Rs. 500

  4. Rs. 600

  5. Rs. 700
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let initial salaries be 5x, 8x, 7x. After increment: (5x+500)/(8x+500) = 10/13. Solving: 65x + 6500 = 80x + 5000 => 15x = 1500 => x = 100. Raj's initial salary = 8x = 800.

Multiple choice

A clerk was asked to give the refund amount of Rs. 129 to three students A, B and C in the ratio 14 : 12 : 17. Due to some miscalculation, money was divided in the ratio 20 : 12 : 11. Who got more money and by how much than asked (in Rs.)?

  1. A, 20

  2. A, 40

  3. A, 18

  4. A, 24

  5. A, 26
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total = 129. Original shares: A=42, B=36, C=51 (Ratio 14:12:17, sum=43). New shares: A=60, B=36, C=33 (Ratio 20:12:11, sum=43). A got 60 - 42 = 18 more.

Multiple choice

Rs. 84,812 is divided between Rani and Raja in the ratio 5 : 8. What is the difference between 6 times the share of Rani and 5 times the share of Raja?

  1. Rs. 66,200

  2. Rs. 95,720

  3. Rs. 60,480

  4. Rs. 65,240

  5. Rs. 3,49,220
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total parts = 5 + 8 = 13. One part = 84812 / 13 = 6524. Rani's share = 5 * 6524 = 32620. Raja's share = 8 * 6524 = 52192. Difference = 6 * 32620 - 5 * 52192 = 195720 - 260960 = -65240. The magnitude of the difference is 65240.

Multiple choice

In a factory, men, women and children were employed in the ratio 8 : 5 : 1 to finish a job and their individual wages were in the ratio 5 : 2 : 3. When 20 women were employed, the total daily wages of them all amounted to Rs. 318. Find the total daily wages paid (in rupees) to each category, respectively.

  1. 210, 70 and 38

  2. 240, 60 and 18

  3. 200, 90 and 28

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given the ratio of men, women, and children as 8:5:1 and 20 women, the multiplier is 4. Thus, there are 32 men, 20 women, and 4 children. With wage ratios 5:2:3, let wages be 5x, 2x, and 3x; total daily wage = 32(5x) + 20(2x) + 4(3x) = 160x + 40x + 12x = 212x = 318, so x = 1.5. Total wages are 240, 60, and 18.

Multiple choice

A sum of Rs. 432 is divided among Ramesh, Rajesh and Suresh, such that Ramesh gets Rs. 144 more than Rajesh and Rajesh gets Rs. 72 more than Suresh. Find the ratio of the shares of Ramesh, Rajesh and Suresh, respectively.

  1. 10 : 9 : 2

  2. 2 : 5 : 11

  3. 11 : 5 : 2

  4. 2 : 5 : 13

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

Let Suresh's share be x. Rajesh = x + 72. Ramesh = (x + 72) + 144 = x + 216. Total = x + x + 72 + x + 216 = 3x + 288 = 432. 3x = 144, so x = 48. Suresh = 48, Rajesh = 120, Ramesh = 264. Ratio 264 : 120 : 48 simplifies to 11 : 5 : 2.