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

An amount of money is to be distributed among P, Q and R in the ratio of 6:19:7 respectively. If R gives Rs. 200 of his share to Q, the ratio among P, Q and R becomes 3:10:3 respectively .What was the total amount?

  1. Rs. 6,400

  2. Rs. 12,800

  3. Rs. 3,200

  4. Rs. 3,600
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let shares be 6x, 19x, 7x (total 32x). After R gives 200 to Q: P=6x, Q=19x+200, R=7x-200. New ratio 3:10:3 means (19x+200)/(6x) = 10/3 and (7x-200)/(6x) = 3/6 = 1/2. From first: 57x+600 = 60x, so 3x = 600, x = 200. Total = 32×200 = 6400.

Multiple choice

The monthly incomes of A and B are in the ratio 4 : 3. Each of them saves Rs 600. If the ratio of their expenditure is 3 : 2, then what is the monthly income of A?

  1. Rs 2400

  2. Rs 2000

  3. Rs 1800

  4. Rs 3600
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let incomes be 4x and 3x. Both save 600, so expenditures are 4x-600 and 3x-600. Given expenditure ratio is 3:2, we have (4x-600)/(3x-600) = 3/2. Cross-multiplying: 2(4x-600) = 3(3x-600), giving 8x-1200 = 9x-1800, so x = 600. A's income = 4x = 4×600 = Rs 2400. Verification: A spends 1800, B spends 1200, ratio is 1800:1200 = 3:2 (correct).

Multiple choice

What is the ratio of investments of Pushpendra, Qareem and Ranjeet? I. Total investments are Rs. 12000 in which Pushpendra’s contribution is Rs. 4500 II. Ratio of investments of Pushpendra to Qareem is 4 : 3 and Qareem to Ranjeet is 3 : 1 III. Pushpendra got Rs. 3000 as a profit.

  1. Only I

  2. Both I and III

  3. Only II sufficient

  4. Both I and II

  5. All I, II and III
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement II gives the ratio chain: Pushpendra:Qareem = 4:3 and Qareem:Ranjeet = 3:1. Combining these (using Qareem as the link) gives Pushpendra:Qareem:Ranjeet = 4:3:1. This is sufficient to determine the investment ratio. Statement I gives actual amounts but not the full ratio (we only know Pushpendra's share). Statement III about profit is irrelevant to the investment ratio question.

Multiple choice

The ratio of the income of Ram and Shyam is 4 : 5 and the ratio of their expenditure is 3 : 4. If Ram saves one fourth of his income, then find the ratio of their savings?
  1. $1 : 3$
  2. $1 : 1$
  3. $2 : 3$
  4. $3 : 1$
  5. $3 : 2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Ram's income be 4x and Shyam's income be 5x. Since Ram saves 1/4 of his income, his expenditure is 3/4 × 4x = 3x, so his savings is 4x - 3x = x. The expenditure ratio is 3:4, so Shyam's expenditure is 4/3 × 3x = 4x, making his savings 5x - 4x = x. Therefore, the ratio of their savings is x:x = 1:1.

Multiple choice

Ratio of earnings of Neetu and Bakhsi is 7 : 13. If the earnings of Neetu increased by 25% and those of Bakhsi decreased by 30%, the new ratio of their earnings become 6 : 8. What is Neetu’s earnings ?

  1. Rs. 20000

  2. Rs. 23540

  3. Rs. 25470

  4. Data inadequate

  5. Rs. 27280
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Neetu's earnings = 7x, Bakhsi's earnings = 13x. After 25% increase, Neetu's new earnings = 7x × 1.25 = 8.75x. After 30% decrease, Bakhsi's new earnings = 13x × 0.70 = 9.1x. The new ratio 8.75x : 9.1x simplifies to 875 : 910 = 175 : 182, which does NOT equal 6 : 8 (which simplifies to 3 : 4 = 0.75). The given ratio 6:8 would require 8.75x/9.1x = 0.9615, but 6/8 = 0.75. The data is inconsistent.

Multiple choice

Rs. 1470 is distributed among Dipti, Anil and Poly in such a way that if each part is reduced by Rs. 50, the ratio becomes 1 : 3 : 2. What is the amount got by Poly?

  1. Rs. 560

  2. Rs. 520

  3. Rs. 490

  4. Rs. 440

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

Let the reduced amounts be in ratio 1:3:2, so Dipti:Anil:Poly = x:3x:2x. After adding Rs. 50 back: Dipti = x+50, Anil = 3x+50, Poly = 2x+50. Sum = 6x + 150 = 1470, so x = 220. Poly's share = 2x + 50 = 2(220) + 50 = Rs. 490.

Multiple choice

The respective ratio of Anu's, Kamal's and Radha's monthly income is 84:76:89. If Kamal's annual income is Rs. 456000. What is the sum of Anu's and Radha's annual income?

  1. Rs. 1195000

  2. Rs. 983500

  3. Rs. 1130000

  4. Rs. 1038000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Kamal's annual income is Rs. 456,000, so monthly = 456000/12 = Rs. 38,000. Using ratio 84:76:89, if 76 parts = 38000, then 1 part = 500. Anu's monthly = 84 × 500 = 42000, Radha's = 89 × 500 = 44500. Sum of annual incomes = (42000 + 44500) × 12 = 86500 × 12 = Rs. 10,38,000.

Multiple choice

The sum of salary of three persons A,B and C is Rs. 72000. They spend 80, 85 and 75 percent of their salary respectively. If ratio of their savings is 8 : 9 : 20, what is A’s salary?

  1. Rs. 20000

  2. Rs. 16000

  3. Rs. 22000

  4. Rs. 18000

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

Let salaries be A, B, C. A+B+C = 72000. Savings: A saves 20%, B saves 15%, C saves 25%. Given savings ratio 8:9:20, let savings be 8x, 9x, 20x. Then A = 8x/0.2 = 40x, B = 9x/0.15 = 60x, C = 20x/0.25 = 80x. Sum: 40x+60x+80x = 180x = 72000, x = 400. A's salary = 40x = Rs. 16000.

Multiple choice

The monthly income of Maneesh and Abhishek is in the ratio 3 : 5 and the ratio between their expenditures is 5 : 9. If their savings for the month is Rs. 800 and Rs. 1200 respectively then find the monthly income of Abhishek.

  1. Rs.2500

  2. Rs.4500

  3. Rs.3000

  4. Rs.3500
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let incomes be 3x and 5x. Expenditures are 5y and 9y. Maneesh saves 3x - 5y = 800, Abhishek saves 5x - 9y = 1200. Solving: 27x - 45y = 7200 and 25x - 45y = 6000, so 2x = 1200 and x = 600. Abhishek's income = 5x = 3000.

Multiple choice

A sum of money is to be divided among Z, C and M in the respective proportion of 4 : 5 : 6 and another sum to be divided between A and B equally. If the difference between the amount of Z and A is Rs. 2000. What is amount received by B ?

  1. Rs. 100

  2. Rs. 200

  3. Rs. 500

  4. Data Inadequate

  5. Rs. 300
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the amount for Z, C, M be 4x, 5x, 6x (total 15x). Let the second sum be divided as A = B = y. We're told |Z - A| = Rs. 2000, but we don't know the actual sums for either group. Without knowing the total amounts or the ratio between the two sums, we cannot determine B's amount. The problem has insufficient information.

Multiple choice

A sum of money is divided among A, B, C in such a way that 5 times A’s share, 3 times B’s share and 2 times C’s share are equal. The ratio between the share of A, B, C is
  1. $5 : 3 : 2$
  2. $2 : 2 : 5$
  3. $15 : 10 : 6$
  4. $6 : 10 : 15$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given that 5A = 3B = 2C, we can find the ratio A:B:C by taking LCM of 5, 3, 2 which is 30. If 5A = 30, then A = 6. If 3B = 30, then B = 10. If 2C = 30, then C = 15. Therefore, A:B:C = 6:10:15, which matches option D.

Multiple choice

A certain amount of money has to be divided between two persons P and Q in the ratio 5:7. But it was divided in the ratio 2:5, and thereby Q gains Rs. 33. Find the total amount.

  1. 160

  2. 140

  3. 252

  4. 120

  5. 150
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let total amount be x. Intended ratio 5:7 means P should get 5x/12 and Q should get 7x/12. Actual ratio 2:5 means P got 2x/7 and Q got 5x/7. Q's gain = actual - intended = 5x/7 - 7x/12 = (60x - 49x)/84 = 11x/84 = 33. So x = 33×84/11 = 3×84 = Rs. 252. Option C is correct.