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

Men, women and children are employed to work in the proportion of 3 : 2 : 1 and their wages are in the ratio of 5 : 3 : 2. When 90 men are employed, total daily wages of all amount to Rs. 10350. Find the daily wage of one man.

  1. Rs. 115

  2. Rs. 75

  3. Rs. 45

  4. Rs. 57.50
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let number of men, women, children be 3x, 2x, x. Given 3x = 90, so x = 30. Number of women = 60, children = 30. Wages ratio 5:3:2 implies wages are 5y, 3y, 2y. Total wages = 90(5y) + 60(3y) + 30(2y) = 10350. 450y + 180y + 60y = 690y = 10350. y = 15. Man's wage = 5y = 75.

Multiple choice

Aryan and Persian are two brothers who work in a multinational company. The ratio of monthly incomes of Aryan and Persian is 3 : 4 and the ratio of their monthly savings is 2 : 3. It is known that Aryan spends two thirds of his income each month. Which of the following can be the ratio of their monthly expenditures?

  1. 3 : 5

  2. 4 : 5

  3. 5 : 6

  4. 9 : 10
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let incomes be 3k and 4k, and savings be 2s and 3s. Aryan's expenditure is 3k - 2s = (2/3) * 3k = 2k. Thus, 2s = k. Aryan's savings are 2s = k, so Persian's savings are 3s = 1.5k. Persian's expenditure is 4k - 1.5k = 2.5k. The ratio of expenditures is 2k : 2.5k = 4 : 5.

Multiple choice

In a bag, there are coins of 25 paisa, 10 paisa and 5 paisa in the ratio of 1 : 2 : 3. If there are Rs. 30 in all, then how many 5 paisa coins are there?

  1. 50

  2. 100

  3. 150

  4. 200
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total tents = 200. Large = 1/4 * 200 = 50. Small = 150. Income from large = 1/3 * Total. Price_L * 50 = 1/3 * (Price_L * 50 + Price_S * 150). 150 * Price_L = 50 * Price_L + 150 * Price_S. 100 * Price_L = 150 * Price_S. Price_L / Price_S = 150 / 100 = 3/2.

Multiple choice

The monthly incomes of Komal and Asha are in the ratio of 4 : 3. Their monthly expenses are in the ratio of 3 : 2. However, both save Rs. 600 per month. What is their total monthly income?

  1. Rs. 8,400

  2. Rs. 5,600

  3. Rs. 4,200

  4. Rs. 2,800
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let incomes be 4x and 3x. Let expenses be 3y and 2y. 4x - 3y = 600 and 3x - 2y = 600. Solving the system: 8x - 6y = 1200 and 9x - 6y = 1800. Subtracting gives x = 600. Total income = 7x = 4200.

Multiple choice

Directions: Read the following case and answer the following question. Mr. Krishna has recently acquired four companies namely K-Tea, Kun-Tea, Sun-Tree and Ruk-Money. When the results of the companies for the year 2015-16 were placed before him, he found a few interesting things about them. While the total expenses of Sun-Tree were 5 times its profits, sales of Ruk-Money were three times its profits. While the profits of Sun-Tree and Ruk-Money were same, as the profits of Kun-Tea were 20% of its sales. The total expenses of Sun-Tree were Rs. 100,000. The total expenses of K-Tea were 10% less than those of Sun-Tree. (Profits are defined as the difference between sales and total expenditure) What is the ratio of expenses of Sun-Tree and Ruk-Money during the financial year 2015-16?

  1. 2 : 1

  2. 4 : 3

  3. 5 : 2

  4. 3 : 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sun-Tree expenses = 100,000. Profits = 1/5 * 100,000 = 20,000. Sales = 120,000. Ruk-Money profits = 20,000. Sales = 3 * 20,000 = 60,000. Expenses = Sales - Profits = 60,000 - 20,000 = 40,000. Ratio Sun-Tree:Ruk-Money = 100,000:40,000 = 5:2.

Multiple choice

Directions: In this problem, a question is followed by statements marked (I), (II) and (III). Read the statements carefully and determine which of the given statements is/are sufficient/necessary to answer the question. Aksh earns Rs. 4000 more than Ankush does. Who among them saves more? I. Ratio of the salaries of Aksh and Ankush is 4 : 3. II. Aksh saves 15% of his salary and Ankush saves Rs. 3000 per month. III. Sum of their salaries is Rs. 28,000.

  1. All statements together

  2. Only statements I and II

  3. Only statement II and either statement I or statement III

  4. Only statements II and III

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

Statement I gives the ratio of salaries. Statement II gives Aksh's savings rate and Ankush's savings amount. To compare savings, we need the actual salaries, which can be derived from I and III. Statement II is necessary to know the savings amount of Aksh. Thus, we need II and either I or III.

Multiple choice

J, K and L entered into a partnership such that the initial investments of J and K are in the ratio 5 : 3 and the initial investments of K and L are in the ratio 2 : 3. After 4 months, J withdraws Rs. 10,000, while K and L invested additional amount of Rs. 12,000 and Rs. 18,000, respectively. After 4 more months, they invested more money in the ratio 7 : 11 : 7. If the amount invested by J and K together is equal to the amount invested by K and L together at the end of the year, find the total investment made by them initially.

  1. Rs. 10,00,000

  2. Rs. 7,00,000

  3. Rs. 5,00,000

  4. Rs. 1,00,000

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

Let initial investments be J=10k, K=6k, L=9k. After 4 months, J=10k-10000, K=6k+12000, L=9k+18000. After 4 more months, they add more in ratio 7:11:7. The condition J+K = K+L at year end implies J=L at year end. Solving the investment equations leads to 700,000.

Multiple choice

Directions: In the given question, two quantities are given, one as 'Quantity 1' and another as 'Quantity 2'. You have to determine relationship between two quantities and choose the appropriate option. K, L, M, N and O divided Rs. 1,33,056 among themselves. K and N took 5/8th of the money and this money divided among K and N in the ratio of 7 : 8 and rest was divided among L, M and O in the ratio 2 : 19 : 3, respectively. Quantity 1: The share of M Quantity 2: The share of N

  1. Quantity 2 > Quantity 1

  2. Quantity 1 ≥ Quantity 2

  3. Quantity 1 > Quantity 2

  4. Quantity 2 ≥ Quantity 1

  5. Quantity 1 = Quantity 2 or Relation cannot be established.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total = 133056. K+N share = 5/8 * 133056 = 83160. N's share = 8/15 * 83160 = 44352. Rest = 133056 - 83160 = 49896. M's share = 19/24 * 49896 = 39491. Since 44352 > 39491, Quantity 2 > Quantity 1.

Multiple choice

Directions: In this question, two quantities are given, one as 'Quantity 1' and another as 'Quantity 2'. You have to determine the relationship between the two quantities and choose the appropriate option. The ratio of the monthly salaries of Neha and Sunita is 14 : 15 and that of Sunita and Komal is 16 : 17, respectively. The total monthly salary of Neha, Sunita and Komal together is Rs. 1,15,040. Quantity 1: Monthly salary of Sunita. Quantity 2: Average monthly salary of Neha and Komal together

  1. Quantity 1 > Quantity 2

  2. Quantity 1 ≥ Quantity 2

  3. Quantity 2 > Quantity 1

  4. Quantity 2 ≥ Quantity 1

  5. Quantity 1 = Quantity 2 or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

N:S = 14:15, S:K = 16:17. Combined N:S:K = 224:240:255. Total parts = 719. Total = 115040. 1 part = 160. Sunita = 240 * 160 = 38400. Average(N,K) = (224+255)/2 * 160 = 239.5 * 160 = 38320. 38400 > 38320.

Multiple choice

The ratio of monthly income of A and B is 3 : 5. If income of each person is increased by Rs 160, this ratio becomes 25 : 41. What is the A's monthly income before increment?

  1. Rs 3840

  2. Rs 9000

  3. Rs 2720

  4. Rs 1570

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

Let A's income be 3x and B's income be 5x. After adding Rs 160 to each, the ratio becomes 25:41. So (3x+160)/(5x+160) = 25/41. Cross-multiplying: 41(3x+160) = 25(5x+160), giving 123x+6560 = 125x+4000. Solving: 2x = 2560, x = 1280. Therefore A's income = 3x = 3×1280 = Rs 3840.

Multiple choice

The ratio between monthly income of Priya, Alka and Rakhi is 43:60:47. The annual income of Alka is Rs. 360000. What is the sum of annual income of Priya and Rakhi?

  1. Rs. 480000

  2. Rs. 540000

  3. Rs. 520000

  4. Rs. 500000

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

The monthly income ratio is Priya:Alka:Rakhi = 43:60:47. Alka's annual income is Rs. 360000, so monthly income is 360000 ÷ 12 = Rs. 30000. Since 60 parts = Rs. 30000, 1 part = Rs. 500. Priya's monthly = 43 × 500 = 21500, annual = 258000. Rakhi's monthly = 47 × 500 = 23500, annual = 282000. Sum = 258000 + 282000 = Rs. 540000.

Multiple choice

A bag contains Rs. 90 in coins. If coins of 50 paise, 25 paise and 10 paise are in the ratio 2 : 3 : 5. How many 50 paise coins are there in the bag ?

  1. 60

  2. 70

  3. 75

  4. 80

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

Let the number of coins be 2x, 3x, and 5x for 50p, 25p, and 10p respectively. Total value: 0.50(2x) + 0.25(3x) + 0.10(5x) = 90. This simplifies to: x + 0.75x + 0.5x = 90, so 2.25x = 90, giving x = 40. Number of 50p coins = 2x = 2 × 40 = 80. Option A (60) would result from incorrectly solving 2x + 3x + 5x = 90 without considering coin values.