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

Divide Rs. 324.36 into three parts in the proportion of 5 : 6 : 7.

  1. Rs. 108.12, 90.10, 126.14

  2. Rs. 126.14, 108.12, 90.10

  3. Rs. 90.10, 108.12, 126.14

  4. Rs. 121.50, 104.98, 71.22
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The sum of the ratio parts is 5 + 6 + 7 = 18. Each part equals 324.36 / 18 = 18.02. The three parts are 5 * 18.02 = 90.10, 6 * 18.02 = 108.12, and 7 * 18.02 = 126.14.

Multiple choice

The ratio of the incomes of two employees is 7 : 4, and the ratio of their expenditures is 3 : 1. If each of them manages to save Rs. 4,800 per month, find the sum of their monthly incomes (in Rs.).

  1. 21,120

  2. 20,120

  3. 21,150

  4. 18,150
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let incomes be 7x and 4x, expenditures 3y and y. Savings: 7x - 3y = 4800 and 4x - y = 4800. From the second, y = 4x - 4800. Substitute into the first: 7x - 3(4x - 4800) = 4800, so 7x - 12x + 14400 = 4800, -5x = -9600, x = 1920. Total income = 11x = 11 * 1920 = 21120.

Multiple choice

A sum of Rs. 2,50,000 is divided among three individuals - X, Y, and Z - in such a way that they receive amounts in the ratio of 3 : 4 : 5, respectively. X further invests his share in a scheme that offers a simple interest rate of 8% per annum for 2 years. Y invests his share in a scheme that offers a compound interest rate of 10% per annum for 3 years. Z keeps his share as cash. Determine the total interest earned by X and Y, after the specified time period.

  1. Rs. 49,180.54

  2. Rs. 37,583.33

  3. Rs. 29,180.54

  4. Rs. 20,180.54
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total sum is 2,50,000. Ratio 3:4:5 means total parts = 12. X's share = (3/12)*2,50,000 = 62,500. Y's share = (4/12)*2,50,000 = 83,333.33. Interest for X (SI) = 62,500 * 0.08 * 2 = 10,000. Interest for Y (CI) = 83,333.33 * ((1.1)^3 - 1) = 83,333.33 * 0.331 = 27,583.33. Total interest = 10,000 + 27,583.33 = 37,583.33.

Multiple choice

Olivia has a total sum of Rs. 10,000, and she allocates it between two banks, A and B, in the ratio of 2 : 3. The rates of interest for these investments in Banks A and B, compounded annually, are in the ratio of 1 : 2. After two years, Olivia receives a total interest of Rs. 1,670. Determine the rate of interest for Bank A.

  1. 4%

  2. 5%

  3. 7%

  4. 8%

  5. 9%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Investment A = 4000, B = 6000. Let rate for A be r, then B is 2r. Interest = 4000((1+r)^2 - 1) + 6000((1+2r)^2 - 1) = 1670. Solving for r: 4000(2r + r^2) + 6000(4r + 4r^2) = 1670. 8000r + 4000r^2 + 24000r + 24000r^2 = 1670. 28000r^2 + 32000r - 1670 = 0. Solving gives r = 0.05 or 5%.

Multiple choice

Ramesh divides 2 plots among his five daughters Meena, Sita, Rekha, Geeta, and Rani. The first plot is divided in the ratio 3 : 2 : 4 : 1 : 5, and the second plot in the ratio 2 : 3 : 1 : 5 : 4. If the second plot is three times the size of the first, then which daughter receives the largest share of plot?

  1. Meena

  2. Sita

  3. Rani

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

Let plot 1 size = P, plot 2 size = 3P. Total shares in plot 1 = 3+2+4+1+5 = 15. Total shares in plot 2 = 2+3+1+5+4 = 15. Rani's share = (5/15)P + (4/15)3P = (5/15)P + (12/15)P = 17/15P. Comparing others: Meena = 3/15P + 6/15P = 9/15P. Sita = 2/15P + 9/15P = 11/15P. Rekha = 4/15P + 3/15P = 7/15P. Geeta = 1/15P + 15/15P = 16/15P. Rani has the largest.

Multiple choice

Directions: In this question, you have to decide which of the statements I, II and III is/are required for determining the answer to the given question. What is the cost price if the product is sold at a profit of 30%? I. The difference between the cost price and the selling price is Rs. 60. II. The ratio of the selling price to the cost price is 13 : 10. III. The selling price is 30% more than the cost price.

  1. Only I

  2. Only I and II

  3. Only II and III

  4. Only II and either I or III

  5. All are insufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To find the actual cost price, we need at least one absolute monetary value. Statement I provides the absolute difference between the selling price and cost price (which is the profit of Rs. 60), allowing us to calculate the cost price as 60 / 0.30 = Rs. 200. Statements II and III only provide ratios or percentages that are already implied by the question.

Multiple choice

Rs. 8400 is divided among A, B, C and D in such a way that the shares of A andB, B and C, and C and D are in the ratios of 2:3, 4:5 and 6:7 respectively. The share of Ais

  1. Rs. 1280

  2. Rs. 8400

  3. Rs. 8210

  4. Rs. 1320

  5. none
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A:B = 2:3 = 8:12, B:C = 4:5 = 12:15, C:D = 6:7. To link them, use common B: 8:12:15. Then C:D = 6:7 = 15:17.5. Ratio A:B:C:D = 8:12:15:17.5. Sum of parts = 52.5. Share of A = (8/52.5) * 8400 = 1280.