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

Price of each article of type P, Q, and R is Rs. 300, Rs. 180 and Rs. 120respectively. Suresh buys articles of each type in the ratio 3:2:3 in Rs. 6480. How manyarticles of type Q did he purchase?

  1. 8

  2. 14

  3. 20

  4. 30

  5. 40
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the number of articles be 3x, 2x, and 3x. The total cost is 300(3x) + 180(2x) + 120(3x) = 900x + 360x + 360x = 1620x. Setting 1620x = 6480, we find x = 4. The number of type Q articles is 2x = 2(4) = 8.

Multiple choice

Priya decides to invest her savings of Rs. 20,000 in two different banks. She deposits the money in a savings account at Bank X, which offers a simple interest rate of 4% per annum. After this investment matures, she reinvests the total amount (initial deposit + interest earned) in a fixed deposit account at Bank Y, where it is kept for 4 years at a simple interest rate of 7% per annum. The interest earned from Bank X to the interest earned from Bank Y is in the ratio 25 : 42. How long did Priya invest her money in Bank X?

  1. 4 years

  2. 5 years

  3. 6 years

  4. 6.5 years

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

Let x be years in Bank X. Interest X = 20000 * 0.04 * x = 800x. Total amount = 20000 + 800x. Interest Y = (20000 + 800x) * 0.07 * 4 = 5600 + 224x. Ratio 800x / (5600 + 224x) = 25/42. 33600x = 25(5600 + 224x) = 140000 + 5600x. 28000x = 140000. x = 5.

Multiple choice

The value of 8% of a gadget's selling price equals 10% of its cost price. Furthermore, 15% of the selling price exceeds 18% of the cost price by Rs. 90. Determine the ratio of the cost price to the selling price.

  1. 3 : 5

  2. 3 : 4

  3. 5 : 4

  4. 4 : 5

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

0.08S = 0.10C => S/C = 10/8 = 5/4. 0.15S - 0.18C = 90. Substitute S = 1.25C: 0.15(1.25C) - 0.18C = 90 => 0.1875C - 0.18C = 90 => 0.0075C = 90 => C = 12000. S = 15000. Ratio C:S = 12000:15000 = 4:5.

Multiple choice

A fruit vendor has one unit each of five different types of fruits: Apples (A1), Bananas (B1), Cherries (C1), Dates (D1), and Elderberries (E1). The prices of A1, B1, and C1 are in the ratio 5 : 6 : 4, while the prices of B1, D1, and E1 are in the ratio 8 : 9 : 10. If D1 costs Rs. 14 more than A1, then what is the total cost (in Rs.) of all the five types of fruits?

  1. Rs. 240

  2. Rs. 270

  3. Rs. 134

  4. Rs. 234

  5. Rs. 284
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From the ratios, A1:B1:C1 = 5:6:4 and B1:D1:E1 = 8:9:10. To combine these, normalize B1 to 24 (the LCM of 6 and 8). Then A1:B1:C1 = 20:24:16 and B1:D1:E1 = 24:27:30. Given D1 - A1 = 14, we have 27x - 20x = 14, so 7x = 14, x = 2. The total sum is (20+24+16+27+30) * 2 = 117 * 2 = 234.

Multiple choice

An amount of Rs. 12,000 is deposited in bank P for a certain number of years at a simple interest rate of 7% per annum. On maturity, the total amount received is deposited in bank Q for another 10 years at a simple interest rate of 8% per annum. If the interests received from bank P and bank Q are in the ratio 35 : 68, then the investment period, in years, in bank P is

  1. 6

  2. 8

  3. 10

  4. 12

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

Interest P = (12000 * 7 * T) / 100 = 840T. Amount P = 12000 + 840T. Interest Q = (Amount P * 8 * 10) / 100 = 0.8 * (12000 + 840T). Ratio = 840T / (0.8 * (12000 + 840T)) = 35/68. Solving for T gives 10.

Multiple choice

Sonali buys 2 Pen Drives A and B and their cost price is in the ratio of 5:6 respectively. If she sells them at a 10% profit each, she earns a total profit of Rs. 22. What will be her total profit, if she sells Pen Drive A at a 20% loss and Pen Drive B at a 30% profit?

  1. Rs. 16

  2. Rs. 13

  3. Rs. 14

  4. Rs. 24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let CP of A = 5x, B = 6x. Profit = 0.1(5x) + 0.1(6x) = 1.1x = 22, so x = 20. CP of A = 100, B = 120. New profit = -0.2(100) + 0.3(120) = -20 + 36 = 16.

Multiple choice

Shruti purchased several number of three articles P, Q and R in the proportion 3 : 2 : 3. If the unit costs of the articles P, Q and R are 200, Rs. 90 and Rs. 60 respectively, how many articles of Q must have been purchased in the total purchases of Rs. 4800?

  1. 8

  2. 10

  3. 12

  4. 14
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the number of articles be 3x, 2x, 3x. Total cost = 3x(200) + 2x(90) + 3x(60) = 600x + 180x + 180x = 960x. 960x = 4800, so x = 5. Number of articles Q = 2x = 2(5) = 10.

Multiple choice

DIRECTION for the question: Solve the following question and mark the best possible option. Rs. 8400 is divided among A, B, C, and D in such a way that the shares of A and B, B and C as well as C and D are in the ratios of 2:3, 4:5, and 6:7 respectively. What will be the share of A?

  1. 1280

  2. 1320

  3. 8210

  4. 8400

  5. 4200
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A:B = 2:3, B:C = 4:5, C:D = 6:7. Normalize ratios: A:B = 16:24, B:C = 24:30, C:D = 30:35. A:B:C:D = 16:24:30:35. Sum = 105 parts. A's share = (16/105) * 8400 = 16 * 80 = 1280.

Multiple choice

DIRECTION for the question: Solve the following question and mark the best possible option. The ratio of incomes of two persons is 5:3 and that of their expenditures is 9:5. If they save Rs 2600 and Rs 1800 respectively, their incomes are

  1. 9000, 5400

  2. 10000, 6000

  3. 6000, 3600

  4. 8000, 4800

  5. 2600, 1800
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let incomes be 5x and 3x. Expenditures are 9y and 5y. 5x - 9y = 2600 and 3x - 5y = 1800. Solving this system: multiply first by 5 and second by 9: 25x - 45y = 13000 and 27x - 45y = 16200. Subtracting gives 2x = 3200, x = 1600. Incomes are 5*1600 = 8000 and 3*1600 = 4800.