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 monthly incomes of S and V are in the ratio of 7 : 5. Their monthly expenditures are in the ratio of 5 : 4. If the savings of S and V are Rs. 2000 and Rs. 1000 respectively, find the income of V?

  1. 7000

  2. 3000

  3. 5000

  4. 2950

  5. 2990
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let incomes be 7x and 5x. Expenditures are 5y and 4y. 7x - 5y = 2000 and 5x - 4y = 1000. Solving the system: 28x - 20y = 8000 and 25x - 20y = 5000. Subtracting gives 3x = 3000, so x = 1000. Income of V = 5x = 5000.

Multiple choice

The monthly Incomes of Ram and Shyam are in the ratio 8 : 5. Their monthly expenses are in the ratio 5:3. Each of them has a monthly saving of Rs. 200. Find the monthly income of Ram(in Rs. ) ?

  1. 2700

  2. 3200

  3. 3000

  4. 2800

  5. 1100
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let incomes be 8x and 5x. Expenses are 5y and 3y. Savings = Income - Expense = 200. 8x - 5y = 200 and 5x - 3y = 200. Multiply first by 3 and second by 5: 24x - 15y = 600 and 25x - 15y = 1000. Subtracting: x = 400. Ram's income = 8x = 8 * 400 = 3200.

Multiple choice

A, B and C intended to divide a certain sum among themselves In the ratio 2 : 3 : 4. By mistake, they divided it in the ratio 1/2 : 1/3 : 1/4 . How many of A, B and C lost due to this mistake?

  1. 0

  2. 2

  3. 1

  4. 3

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

Original ratio 2:3:4 means shares are 4/18, 6/18, 8/18 of the total. Mistake ratio 1/2:1/3:1/4 is 6:4:3, meaning shares are 6/13, 4/13, 3/13. Comparing 4/18 (approx 0.22) vs 6/13 (approx 0.46) for A, 6/18 (0.33) vs 4/13 (0.30) for B, and 8/18 (0.44) vs 3/13 (0.23) for C. A gained, B lost, C lost. Two people lost.

Multiple choice

Three friends P, Q and R divide \$1105 amongst them in such a way that if \$10, $20 and $15 are removed from the sums that P, Q and R received respectively, then the share of the sums that they got will be in the ratio of 11 : 18 : 24. How much did R receive?
  1. $495
  2. $510
  3. $480
  4. $375
  5. $360
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total remaining = 1105 - (10+20+15) = 1060. Ratio 11:18:24. Sum of parts = 11+18+24 = 53. One part = 1060 / 53 = 20. R's share = 24 * 20 + 15 = 480 + 15 = 495.

Multiple choice

Incomes of A and B are in the ratio 3 : 4. The expenditures are in the ratio 4 : 5. Find the ratio of the savings if B saves one - third of his income ?

  1. 13 : 21

  2. 13 : 20

  3. 14 : 23

  4. 12 : 19

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

Income ratio 3x:4x. Expenditure ratio 4y:5y. Savings = Income - Expenditure. B saves 1/3 of income: 4x - 5y = (1/3)*4x => 12x - 15y = 4x => 8x = 15y => y = 8x/15. Savings A = 3x - 4(8x/15) = 3x - 32x/15 = 13x/15. Savings B = 4x/3 = 20x/15. Ratio 13:20.

Multiple choice

Directions: Solve the following question and mark the best possible option. Suppose, C1, C2, C3, C4, and C5 are five companies. The profits made by C1, C2, and C3 are in the ratio 9 : 10 : 8 while the profits made by C2, C4, and C5 are in the ratio 18 : 19 : 20. If C5 has made a profit of Rs. 19 crore more than C1, then the total profit (in Rs) made by all five companies is

  1. 438 crore

  2. 435 crore

  3. 348 crore

  4. 345 crore
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ratios: C1:C2:C3 = 9:10:8. C2:C4:C5 = 18:19:20. Normalize C2 to 90: C1:C2:C3 = 81:90:72. C2:C4:C5 = 90:95:100. C5 - C1 = 100k - 81k = 19k = 19 crore. k = 1. Total = 81+90+72+95+100 = 438.