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

Points A and B are both in the line segment PQ and on the same side of its midpoint. A divides PQ in the ratio 2:3, and B divides PQ in the ratio 3:4. If AB = 2, then the length of PQ is-

  1. 70

  2. 75

  3. 80

  4. 85

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

Let PQ = x. Point A divides PQ in ratio 2:3, so A is at (2/5)x from P. Point B divides PQ in ratio 3:4, so B is at (3/7)x from P. Since both are on the same side of the midpoint, the distance AB = (3/7)x - (2/5)x = (15/35 - 14/35)x = (1/35)x. Given AB = 2, we have (1/35)x = 2, so x = 70. Therefore, PQ = 70.

Multiple choice

Hridaya opened her piggy bank and found coins of denominations Rs. 1, Rs. 2, Rs. 5 and Rs. 10 in the ratio 10 : 5 : 2 : 1. If there are 72 coins in all, then how much money (in Rs.) was there in the piggy bank in the form of coins?

  1. 160

  2. 72

  3. 90

  4. 100
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ratio is 10:5:2:1, so total parts = 18. Each part = 72/18 = 4 coins. Rs. 1: 40 coins, Rs. 2: 20 coins, Rs. 5: 8 coins, Rs. 10: 4 coins. Total = 40×1 + 20×2 + 8×5 + 4×10 = 40 + 40 + 40 + 40 = Rs. 160. The pattern is that each denomination contributes the same amount (Rs. 40) to the total because the ratio is weighted inversely to denomination value.

Multiple choice

A sum of Rs. 31866 is divided between A, B and C such that the ratio of shares of A and B is 9 : 8 and that of A and C is 4 : 5, The share (in Rs.) of B is:

  1. 9024

  2. 10254

  3. 8546

  4. 9224
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To find B's share, first determine the combined ratio A:B:C. Given A:B = 9:8 and A:C = 4:5, make A's part equal by converting to A:B = 36:32 and A:C = 36:45. This gives A:B:C = 36:32:45, where the total is 113 parts. B's share is (32/113) × 31866 = 9024.

Multiple choice

Antony decided that when he retires, he will put 25% of his retirement money in the share market, 20% will be given to an orphanage, 5% to an old age home and the rest will be distributed among his three children Sara, John, and Bill in the ratio 2 ∶ 2 ∶ 1. If Bill received Rs. 25,000 find the money he invested in the share market?

  1. Rs. 50,000

  2. Rs. 52,500

  3. Rs. 60,000

  4. Rs. 62,500

  5. Rs. 65,500
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total allocated: 25% + 20% + 5% = 50%. Remaining 50% is distributed among children in ratio 2:2:1 (total 5 parts). Bill gets 1/5 of 50% = 10%. If 10% = Rs. 25,000, then 100% = Rs. 2,50,000. Share market investment = 25% of Rs. 2,50,000 = Rs. 62,500.

Multiple choice

The train ticket fare from places A to B in 2nd class AC and 3rd class AC is Rs. 2,500 and Rs. 2,000, respectively. If the fares of 2nd class AC and 3rd class AC are increased by 20% and 10%, respectively, then find the ratio of the new fares of 2nd class AC and 3rd class AC.
  1. $13 : 11$
  2. $15 : 11$
  3. $11 : 15$
  4. $12 : 11$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original fares: 2nd class = Rs. 2,500, 3rd class = Rs. 2,000. New 2nd class = 2500 × 1.20 = Rs. 3,000. New 3rd class = 2000 × 1.10 = Rs. 2,200. New ratio = 3000:2200 = 30:22 = 15:11. Always apply percentage changes first, then simplify the ratio to lowest terms.

Multiple choice

A sum of Rs. 11,236 is divided among A, B and C such that the ratio of the shares of A and B is (3 ∶ 5) and the ratio of the shares of A and C is (4 ∶ 7). The share of B is: (in Rs.)

  1. 4452

  2. 3392

  3. 4240

  4. 2544
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From A:B = 3:5, let A = 3k and B = 5k. From A:C = 4:7, C = (7/4)A = (7/4) × 3k = 21k/4. Total: 3k + 5k + 21k/4 = 8k + 5.25k = 13.25k = 53k/4 = 11236. So k = 11236 × 4/53 = 424. B's share = 5k = 5 × 424 = 2120. Wait - let me recalculate: 3k + 5k + 21k/4 = (8k × 4 + 21k)/4 = 53k/4 = 11236, so k = 11236 × 4/53 = 848. B = 5k = 4240.

Multiple choice

The ratio of the monthly incomes of three employees, Saloni, Reema and Kalyani, is 54 : 21 : 59, respectively. If Reema’s annual income is Rs. 5,04,000, what is the sum of Saloni’s and Kalyani’s annual income?

  1. Rs. 27,21,000

  2. Rs. 21,72,000

  3. Rs. 21,27,000

  4. Rs. 27,12,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Monthly income ratio is 54 : 21 : 59. Reema's annual income = Rs. 5,04,000, so her monthly income = 5,04,000 ÷ 12 = Rs. 42,000. If 21 parts = Rs. 42,000, then 1 part = Rs. 2,000. Saloni (54 parts) = 54 × 2,000 = Rs. 1,08,000 monthly, annual = Rs. 12,96,000. Kalyani (59 parts) = 59 × 2,000 = Rs. 1,18,000 monthly, annual = Rs. 14,16,000. Sum = Rs. 12,96,000 + Rs. 14,16,000 = Rs. 27,12,000.

Multiple choice

If the ratio of monthly income of A and B is 16: 17 . if they get 4500 Rs as a bonus the ratio of their income become 19 :20 . find the monthly income of A ?

  1. 24000

  2. 25000

  3. 26000

  4. 20000

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

Let monthly incomes be 16x and 17x. After bonus of 4500: (16x + 4500) ÷ (17x + 4500) = 19 ÷ 20. Cross-multiply: 20(16x + 4500) = 19(17x + 4500). 320x + 90000 = 323x + 85500. 90000 - 85500 = 323x - 320x. 4500 = 3x. x = 1500. A's income = 16x = 16 × 1500 = 24000.

Multiple choice

The salary of A man is Rs. 50000 per month from which he spends 20% on rent, 10% of remaining on bills, 20% of further remaining on miscellaneous expenses. From the remaining amount, man gives some money to his wife and rest he invests in mutual funds in the ratio of 5: 4. Find amount spent on rent is how much less or more than amount invested in mutual funds?

  1. 2800 Rs.

  2. 2400 Rs.

  3. 2600 Rs.

  4. 3200 Rs.

  5. 3000 Rs.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

After 20% rent from 50000: 50000 - 10000 = 40000. After 10% bills: 40000 - 4000 = 36000. After 20% miscellaneous: 36000 - 7200 = 28800. This is split 5:4 (9 parts), so mutual fund gets (4/9) × 28800 = 12800. Rent (10000) is 2800 less than mutual fund investment (12800).

Multiple choice

A man deposits 10% of his salary in a Mutual fund. He saves 30% of the remaining. The ratio of his expense on medicine and groceries is 5:4 of the remaining salary after saving. If his expense on medicine was Rs 7000. Find the monthly salary?

  1. 28000 Rs.

  2. 40000 Rs.

  3. 20000 Rs.

  4. 32000 Rs.

  5. 60000 Rs.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let salary = x. Mutual fund = 0.1x, remaining = 0.9x. Savings = 30% of 0.9x = 0.27x. Amount after savings = 0.9x - 0.27x = 0.63x. Medicine : Groceries = 5:4, so medicine = (5/9) × 0.63x = 0.35x = Rs 7000. Therefore x = 7000/0.35 = Rs 20000.

Multiple choice

Price of a diamond is directly proportional to the square of its weight. If the diamond break into 3 pieces by mistake, the ratio of their weight becomes 1 : 2 : 3 : therefore loss will arise Rs 440,00. Find original price of the diamond? हीरे की कीमत उसके वजन के वर्ग के सीधे आनुपातिक होती है। यदि गलती से हीरा 3 टुकड़ों में टूट जाता है, तो उनके वजन का अनुपात 1:2:3 हो जाता है: इसलिए नुकसान 440,00 रुपये होगा। हीरे की वास्तविक कीमत ज्ञात कीजिए?

  1. Rs 36000 36000 रुपये

  2. Rs 72000 72000 रुपये

  3. Rs 22000 22000 रुपये

  4. Rs 18000 18000 रुपये

  5. Rs 16500 16500 रुपये
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let original weight be 6x and price be k(6x)² = 36kx². When broken into pieces with weights 1x, 2x, 3x, their prices are kx², 4kx², 9kx² totaling 14kx². Loss = 36kx² - 14kx² = 22kx² = Rs 44,000. Original price = 36kx² = (36/22) × 44,000 = Rs 72,000.

Multiple choice

The amount that A and B earns is in the ratio 4 : 3. After a year, A’s salary got increased by 25% and B’s salary by 33.33%. If now the total of their salaries become Rs 8100, What was the initial salary of A? A और B की कमाई का अनुपात 4:3 है। एक साल बाद, A के वेतन में 25% और B के वेतन में 33.33% की वृद्धि हुई। यदि अब उनका कुल वेतन 8100 रुपये हो जाता है, तो A का प्रारंभिक वेतन कितना था?

  1. 3600

  2. 1200

  3. 2400

  4. 2000

  5. 1600
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let initial salaries be 4x and 3x. After increase: A's salary = 4x + 25% of 4x = 5x. B's salary = 3x + 33.33% of 3x = 4x. Total new salary = 9x = 8100. So x = 900. A's initial salary = 4x = 3600.

Multiple choice

Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B is दो संख्याएँ A और B इस प्रकार हैं कि A के 5% और B के 4% का योग A के 6% और B के 8% के योग का दो-तिहाई है। A : B का अनुपात ज्ञात कीजिए

  1. 4:1

  2. 9:8

  3. 5:2

  4. 4:3

  5. 1:2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given: 5% of A + 4% of B = 2/3(6% of A + 8% of B). This gives 0.05A + 0.04B = 2/3(0.06A + 0.08B) = 0.04A + 0.0533B. Rearranging: 0.05A - 0.04A = 0.0533B - 0.04B, giving 0.01A = 0.0133B, so A/B = 1.333/1 = 4/3. Therefore A:B = 4:3.