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 cost of two books are in the ratio $3\colon 5$. If the cost of each of them increases by $Rs.\,20$, the ratio is altered to $13\colon 21$. What is the initial cost of each of them?
  1. $Rs.\ 240$ and $Rs.\ 400$
  2. $Rs.\ 260$ and $Rs.\ 420$
  3. $Rs.\ 280$ and $Rs.\ 440$
  4. $Rs.\ 200$ and $Rs.\ 360$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let costs be 3x and 5x. (3x + 20) / (5x + 20) = 13 / 21. 21(3x + 20) = 13(5x + 20). 63x + 420 = 65x + 260. 2x = 160, x = 80. Costs are 3*80=240 and 5*80=400.

Multiple choice

The ratio of first and second class train fares between two station is $3:1$ and that of the number of passengers travelling between these stations by first and second class is $1:50.$ If on a particular day $Rs. 1325$ be collected from the passengers travelling between these stations, then the amount collected from the second class passengers is:
  1. $Rs. 1250$
  2. $Rs. 1000$
  3. $Rs. 850$
  4. $Rs. 750$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ratio of fares = 3:1. Ratio of passengers = 1:50. Ratio of total collection = (3*1) : (1*50) = 3:50. Total parts = 53. Total collection = 1325. One part = 1325 / 53 = 25. Second class collection = 50 * 25 = 1250.

Multiple choice

Rs 180 is to be divided among 66 persons (men and women) The ratio of the total amount of money received by men and women is 5 : 4 But the ratio of the money received by each man and woman is 3 : 2 The number of men is

  1. 20

  2. 24

  3. 30

  4. 36
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let M be number of men, W be number of women. M+W=66. Ratio of total money M:W = 5:4. Ratio of individual money m:w = 3:2. Total money for men = M*m, for women = W*w. (M*3)/(W*2) = 5/4. 12M = 10W, so 6M = 5W. W = 1.2M. M + 1.2M = 66. 2.2M = 66. M = 30.

Multiple choice

One day the ratio of the number of first class and second class passengers who travelled were in the ratio 1 : 30 The ratio of the first and second class fares is 3 : 1 The total amount collected from the passengers that day was Rs 66000 Find the amount collected from the first class passengers (in Rs)

  1. Rs 3000

  2. Rs 6000

  3. Rs 9000

  4. Rs 12000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let passengers be 1x and 30x. Fares are 3y and 1y. Total = (1x * 3y) + (30x * 1y) = 3xy + 30xy = 33xy = 66000. xy = 2000. First class collection = 3xy = 3 * 2000 = 6000.

Multiple choice

A man divides his property so that his son's share to his wife's and the wife's share to his daughter are both in the ratio $3:1$. If the daughter gets $10,000$ less than the son, find the total worth of the property.
  1. $15,000$
  2. $16,250$
  3. $20,000$
  4. $25,000$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let daughter's share = x. Wife's share = 3x. Son's share = 3(3x) = 9x. Total = 13x. Given 9x - x = 10000, 8x = 10000, x = 1250. Total property = 13 * 1250 = 16250.

Multiple choice

A purse contains some coins consisting of rupees, fifty paise coins and twenty-five paise coins. If coins be in the ratio of $2:3:10$ and their total value is Rs. $72$, the number of twenty-five paise coins will be.
  1. $100$
  2. $140$
  3. $120$
  4. $80$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the number of coins be 2x, 3x, and 10x. Value = 100(2x) + 50(3x) + 25(10x) = 200x + 150x + 250x = 600x paise = 6x rupees. 6x = 72 => x = 12. Number of 25 paise coins = 10x = 10 * 12 = 120.

Multiple choice

If the two friends Robert and James have savings in the ratio $ 6 : 10 $ but due to some urgency each has to spend Rs $40$, so their ratio reduces to $ 1 : 2 $. Find the total amount of saving the two friends have initially.
  1. Rs $260$
  2. Rs $360$
  3. Rs $180$
  4. Rs $320$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let initial savings be 6x and 10x. (6x - 40) / (10x - 40) = 1/2. Cross-multiply: 12x - 80 = 10x - 40. 2x = 40, so x = 20. Total initial savings = 16x = 16 * 20 = 320.