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

4 boys and 8 girls can finish a job in 20 hours, while 8 boys and 10 girls can finish the same job in 12 hours. The pay-out is given to them according to their outputs. If a boy gets Rs. 160 per hour, then what is the ratio of the per hour pay-outs of a boy to that of a girl?

  1. 1 : 1

  2. 5 : 4

  3. 5 : 3

  4. 5 : 2

  5. 5 : 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let B and G be the hourly pay of a boy and a girl. 20(4B + 8G) = 12(8B + 10G). 80B + 160G = 96B + 120G. 40G = 16B. B/G = 40/16 = 5/2.

Multiple choice

A sum of money has been distributed among four friends in such a way that the proportion of shares is 1 : 2 : 3 : 8. If the third friend gets Rs. 300 less than the fourth friend gets, then find the second friend's share.

  1. Rs. 120

  2. Rs. 54.40

  3. Rs. 50

  4. Rs. 20

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

Let the shares be 1k, 2k, 3k, 8k. The difference between the third and fourth friend is 8k - 3k = 5k = 300, so k = 60. The second friend's share is 2k = 2(60) = 120.

Multiple choice

Jack, Lily and Moly jointly contributed a sum of Rs. 12,000 in a certain ratio. Out of this amount they spent sums of Rs. 300, 400 and 300 individually. Their contribution in the remaining amount was in the ratio 2 : 4 : 4. What was Moly's share in the initial amount?

  1. Rs. 2300

  2. Rs. 5400

  3. Rs. 4700

  4. Rs. 4500

  5. Rs. 5800
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total spent = 300 + 400 + 300 = 1000. Remaining amount = 12000 - 1000 = 11000. The ratio 2:4:4 means Moly's share of the remainder is 4/10 * 11000 = 4400. Adding back her individual spend of 300, her initial share = 4400 + 300 = 4700.

Multiple choice

The incomes of A and B are in the ratio 2 : 3 and their expenditures are in the ratio 1 : 2. If each saves Rs. 24,000, find A's income.

  1. Rs. 24,000

  2. Rs. 72,000

  3. Rs. 19,200

  4. Rs. 48,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let incomes be 2x and 3x, and expenditures be 1y and 2y. Savings are Income - Expenditure: 2x - y = 24000 and 3x - 2y = 24000. Multiplying the first by 2 gives 4x - 2y = 48000. Subtracting the second from this gives x = 24000. A's income is 2x = 48000.

Multiple choice

If the persons A and B have incomes in the ratio 7 : 5 and expenditures in the ratio 3 : 2 and each one of them saves Rs. R, then, the income of A is:

  1. 7R

  2. 7R/2

  3. 14R

  4. R/2

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

Let incomes be 7x and 5x, and expenditures be 3y and 2y. Savings are 7x - 3y = R and 5x - 2y = R. Thus 7x - 3y = 5x - 2y, so 2x = y. Substituting y = 2x into the first equation: 7x - 3(2x) = R, which means x = R. Income of A is 7x = 7R.

Multiple choice

Between two stations, the first, second and third class fares are in the ratio 9 : 7 : 2. The number of passengers travelling in a day are in the ratio 5 : 3 : 2, respectively, in the above classes. If the sale of tickets generated revenue of Rs. 98,000 that day and if 200 passengers travelled by third class, what was the fare for a first class ticket?

  1. 116

  2. 126

  3. 122

  4. 129

  5. 132
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Fares: 9x, 7x, 2x. Passengers: 5y, 3y, 2y. 2y = 200, so y = 100. Passengers are 500, 300, 200. Revenue = (500*9x) + (300*7x) + (200*2x) = 4500x + 2100x + 400x = 7000x. 7000x = 98000, so x = 14. First class fare = 9x = 9 * 14 = 126.

Multiple choice

The ratio of the income of John to that of Danny is 5 : 4 and the ratio of their expenses is 3 : 2. If each of them saves Rs. 1200 at the end of the year, then what is the income of Danny?

  1. Rs. 3000

  2. Rs. 4800

  3. Rs. 1200

  4. Rs. 2400

  5. Rs. 600
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let incomes be 5x and 4x, expenses 3y and 2y. 5x - 3y = 1200 and 4x - 2y = 1200. From the second, 2y = 4x - 1200, so 3y = 6x - 1800. Substitute into the first: 5x - (6x - 1800) = 1200, so -x + 1800 = 1200, x = 600. Danny's income = 4x = 2400.

Multiple choice

A sum of Rs. 570 is divided among 66 persons consisting of men, women and children. The ratio of the sums of the shares of all men, all women and all children is 5 : 6 : 8, but the individual shares of a man, woman and child are in ratio 1 : 3 : 2. Find the share of each one of them (in Rs.).

  1. M-7, W-15, C-12

  2. M-5, W-15, C-10

  3. M-10, W-9, C-8

  4. M-5, W-7, C-12

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

Let M, W, C be the number of men, women, and children. Total = 66. Total money = 570. Shares ratio 5:6:8 means total shares for groups are 5k, 6k, 8k. 5k+6k+8k = 570 => 19k = 570 => k=30. Total money for men = 150, women = 180, children = 240. Individual shares ratio 1:3:2 means M=x, W=3x, C=2x. Total people: 150/x + 180/3x + 240/2x = 66 => 150/x + 60/x + 120/x = 66 => 330/x = 66 => x=5. Individual shares: M=5, W=15, C=10.

Multiple choice

A company has 14 machines of equal efficiency in its factory. The annual manufacturing costs are Rs. 42,000 and establishment charges are Rs. 12,000. The annual output of the company is Rs. 70,000. The annual output and the manufacturing costs are directly proportional to the number of machines. The shareholders get 12.5% profit, which is directly proportional to the annual output of the company. If 7.14% machines remain shut throughout the year, then the percentage decrease in the amount of profit of the shareholders would be

  1. 12.0%

  2. 12.5%

  3. 13.0%

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Directions: The following problem contains a question and three statements giving certain data. You have to decide whether the data given in the statements is sufficient for answering the question and then mark the correct option accordingly. What is the total savings of father per month from his salary? I. His total expenditure is 65% of his salary. II. He spends Rs. 12,500 per month on food and 15% of salary on tuition and saves the remaining amount. III. His salary to expenditure ratio is 10 : 7.

  1. Only II

  2. Only III

  3. Both II and III

  4. Either II or III

  5. None
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Rohit, Raina and Ravindra divide a total sum of Rs. 4860 in such a manner that if their shares were decreased by Rs. 10, Rs. 20 and Rs. 30, respectively, then their remaining amounts would be in the ratio of 3 : 4 : 5. What is Ravindra's share in the initial amount?

  1. Rs. 1210

  2. Rs. 2000

  3. Rs. 2030

  4. Rs. 2025

  5. Rs. 2055
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let remaining amounts be 3x, 4x, 5x. Total = 3x+10 + 4x+20 + 5x+30 = 4860. 12x + 60 = 4860. 12x = 4800. x = 400. Ravindra's share = 5x + 30 = 5(400) + 30 = 2030.

Multiple choice

Two sisters get pocket money in ratio of square roots of their ages. The elder sister is 9 years older than the younger and gets Rs. 250 more as pocket money. If the age of the elder sister had exceeded that of the younger by 4 1 4 years, then their pocket money would have been in the ratio 9 : 8. What are their respective ages?

  1. 17 years and 8 years

  2. 28 years and 19 years

  3. 25 years and 16 years

  4. 47 years and 38 years

  5. 42 years and 30 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the younger sister be y years old. The second condition gives sqrt((y+4.25)/y) = 9/8, so (y+4.25)/y = 81/64, yielding y = 16. The elder sister is then 16+9 = 25 years old, confirming option C.