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

How can 700 be divided in the ratio 2 : 3?

  1. 280, 420

  2. 380, 320

  3. 280, 520

  4. 230, 570
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To divide 700 in the ratio 2:3, the total parts are 2 + 3 = 5. Each part is 700 / 5 = 140. The two shares are 2 * 140 = 280 and 3 * 140 = 420.

Multiple choice

A bag contains one rupee, 50 paise, 25 paise and 10 paise coins in the proportion 1 : 3 : 5 : 7. If the total amount is Rs. 22.25, find the number of coins of each kind.

  1. Rs. 1, 5; 50 paise 25; 25 paise, 15; 10 paise, 25

  2. Rs. 1, 5; 50 paise 15; 25 paise, 25; 10 paise, 35

  3. Rs. 1, 5; 50 paise 25; 25 paise, 15; 10 paise, 35

  4. Rs. 1, 5; 50 paise 25; 25 paise, 25; 10 paise, 25
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the number of coins be 1x, 3x, 5x, 7x. The value is 1(x) + 0.5(3x) + 0.25(5x) + 0.1(7x) = 22.25. This gives x + 1.5x + 1.25x + 0.7x = 4.45x = 22.25. Solving for x gives x = 5. The number of coins are 5, 15, 25, 35.

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. Find the amount received by each man. I. Rs. 140 is divided among 30 persons. II. The ratio of the total amounts of money received by men and women is 4 : 3. III. The ratio of amounts received by each man and woman is 2 : 1.

  1. Only I and II

  2. Only I and either II or III

  3. Only I and III

  4. All I, II and III

  5. Any two of the three statements
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the amount per man, we need the total amount (I), the ratio of total money for men vs women (II), and the ratio of individual amounts (III). With these, we can set up a system of equations to solve for the number of men and women and their respective shares.

Multiple choice

Three friends P, Q and R have a certain amount of money with them in such a way that the ratio of amounts of money with P and Q is 3 : 4 and with Q and R is 5 : 6, respectively. If we multiply the amounts of money with Q and R, we get Rs. 5070 as the answer. Find the total amount of money (in Rs.) with all the friends.

  1. 155.75

  2. 190.50

  3. 191.75

  4. 195.50

  5. 197.75
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P:Q = 3:4, Q:R = 5:6. To combine, multiply P:Q by 5 and Q:R by 4: P:Q:R = 15:20:24. Let amounts be 15x, 20x, 24x. Q*R = 20x * 24x = 480x^2 = 5070. x^2 = 5070 / 480 = 10.5625. x = 3.25. Total = (15+20+24)x = 59x = 59 * 3.25 = 191.75.

Multiple choice

Rs. 2,00,000 is divided amongst four individuals - X, Y, Z, and W - in a manner that allocates to them proportions of 25%, 20%, 35%, and 20%, respectively. Subsequently, X obtains an equivalent sum from a distinct financial pool that is disbursed among them based on proportions of 20%, 35%, 25%, and 20%, respectively. What is the discrepancy in the sums received by Y from both of these allocations?

  1. Rs. 35,500

  2. Rs. 20,500

  3. Rs. 27,500

  4. Rs. 47,500
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

An amount of Rs. 10,000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is

  1. 4

  2. 6

  3. 3

  4. 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let T be the time in Bank A. Interest A = 10000 * 5 * T / 100 = 500T. Amount after A = 10000 + 500T. Interest B = (10000 + 500T) * 6 * 5 / 100 = 3000 + 150T. Ratio 500T / (3000 + 150T) = 10/13. 6500T = 30000 + 1500T, 5000T = 30000, T = 6.

Multiple choice

A young entrepreneur takes a loan of Rs. 1,50,000 from a bank for a period of 6 years to expand his retail store. He borrows part of the amount at an interest rate of 4% per annum under a government-supported loan for small businesses, and the remaining part at 7% per annum under a standard commercial loan. The total interest he has to pay at the end of 6 years is Rs. 41,400. What is the ratio of the loan amount borrowed under the government-supported loan for small businesses to the amount borrowed under the commercial loan?

  1. 2 : 3

  2. 1 : 4

  3. 3 : 2

  4. 4 : 1

  5. 5 : 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total interest for 6 years is 41,400 rupees, which means the interest per year is 6,900 rupees. Let x be the amount borrowed at 4% and (1,50,000 - x) be the amount at 7%. Solving the annual interest equation 0.04x + 0.07(1,50,000 - x) = 6,900 gives x = 1,20,000 rupees, meaning the remaining commercial loan is 30,000 rupees. The ratio of the two amounts is 1,20,000 : 30,000, which simplifies to 4 : 1.

Multiple choice

An amount of Rs. 12,000 is deposited in bank X for a certain number of years at a simple interest rate of 4% per annum. Upon maturity, the total sum is reinvested in bank Y for 5 years at a simple interest rate of 5% per annum. If the interest earned from bank X and bank Y is in the ratio 2 : 3, then the number of years the amount was invested in bank X is:

  1. 4

  2. 5

  3. 6

  4. 7

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

Interest from Bank X = (12000 * 4 * T) / 100 = 480T. The total sum after Bank X is 12000 + 480T. Interest from Bank Y = ((12000 + 480T) * 5 * 5) / 100 = (12000 + 480T) * 0.25 = 3000 + 120T. Ratio (480T) / (3000 + 120T) = 2/3. 1440T = 6000 + 240T. 1200T = 6000. T = 5.

Multiple choice

A juice bar offers drinks in three different bottle sizes. The product of the prices (in Rs.) of the small, medium, and large bottles is Rs. 94,500. The prices of the small and large bottles are in the ratio 3:7. Later, the owner increases the price of the small bottle by Rs. 5 and that of the large bottle by Rs. 20, while keeping the medium bottle's price unchanged. As a result, the product of the new prices becomes Rs. 1,41,750. What is the sum of the original prices (in Rs.) of the three bottle sizes?

  1. 130

  2. 140

  3. 155

  4. 145
Reveal answer Fill a bubble to check yourself
D Correct answer