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

A bag contains 190 coins consisting of Rs. 5, Rs. 2 and Rs. 1 coins. If the ratio of their values be 5 : 6 : 15. Find the number of Rs. 5 coins?

  1. 10

  2. 12

  3. 8

  4. 15

  5. 18
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let number of Rs. 5, Rs. 2, Rs. 1 coins be 5x, 2x, x respectively (values ratio 5:6:15, but number of Rs. 2 coins must be even, so assume value ratio structure: let actual counts be a, b, c where 5a:2b:c = 5:6:15. From ratio 5a:2b:c = 5:6:15, we get 5a/5 = 2b/6 = c/15. Simplifying: a = b/3, c = 3b. If b = 30, then a = 10, c = 90. Total = 10 + 30 + 90 = 130 ≠ 190. Alternative: value ratio means actual values are 5k, 6k, 15k. So 5a = 5k → a = k. 2b = 6k → b = 3k. c = 15k. Total: k + 3k + 15k = 19k = 190 → k = 10. Therefore a = 10 Rs. 5 coins. Option A is correct.

Multiple choice

Shweta, Shubhi and Samta divide an amount of Rs. 8400 amongst themselves in the ratio of 7: 8: 6 respectively. If an amount of Rs. 400 is added to each of their shares, what will be the new respective ratio of their shares of amount?
  1. $5 : 7 : 4$
  2. $3 : 5 : 4$
  3. $9 : 10 : 8$
  4. $10 : 11 : 9$
  5. $8 : 9 : 7$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Original ratio 7:8:6 on sum 8400 gives parts: (7+8+6) = 21 parts, each part = 8400/21 = 400. So original shares are: 7×400 = 2800, 8×400 = 3200, 6×400 = 2400. After adding 400 to each: 2800+400 = 3200, 3200+400 = 3600, 2400+400 = 2800. Simplified ratio: 3200:3600:2800 = 8:9:7 (dividing by 400). Option E is correct.

Multiple choice

The ratio between the incomes of Mohan and Rakesh is 5 : 4 and the ratio between their expenditures is 3 : 2. If at the end of the year both saves Rs. 1600, then find the income of B. मोहन और राकेश की आय का अनुपात 5 : 4 है और उनके खर्चों का अनुपात 3 : 2 है | यदि वर्ष के अंत में दोनों रु 1600 बचाएं, तो B की आय कितनी है ?

  1. 4000

  2. 3500

  3. 3200

  4. 3000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let incomes be 5I and 4I, expenditures be 3E and 2E. Both save 1600, so 4I - 2E = 1600 for Rakesh (person B). Solving gives E = 2I - 800. From Mohan's equation 5I - 3E = 1600, we get I = 800. B's income = 4I = 3200.

Multiple choice

A man incashes a cheque of Rs 600 from a bank.The bank pays him in 10 rupee and 5 rupee notes totalling 72.Find the ratio of the number of 10 rupee notes to that of the 5 rupee notes? एक आदमी चेक भुगतान से एक बैंक से 600 रू. प्राप्त करता है। बैंक उसे 10 रू. और 5 रू. के कुल 72 नोट देता है। 10 रू. के नोटों का 5 रू. के नोटों से अनुपात ज्ञात कीजिए?

  1. 2 : 1

  2. 1 : 3

  3. 3 : 2

  4. 3 : 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x = number of Rs. 10 notes, y = number of Rs. 5 notes. Total: 10x + 5y = 600, so 2x + y = 120. Also x + y = 72. Subtracting: (2x+y) - (x+y) = 120-72, so x = 48. Then y = 72-48 = 24. Ratio x:y = 48:24 = 2:1.

Multiple choice

The total income of A and B is 33000. A and B spend 60% and 75% of his income respectively and their saving is in the ratio 4 : 3. Find the income of A.

  1. Rs. 10,000

  2. Rs. 12000

  3. Rs. 15000

  4. Rs. 18000

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

Let A's income be x and B's income be (33000-x). A saves 40% (spends 60%) and B saves 25% (spends 75%). Their savings ratio is 4:3, so 0.4x/0.25(33000-x) = 4/3. Cross-multiplying: 1.2x = 0.333(33000-x). Solving: x = Rs. 15,000. Verification: A saves Rs. 6,000, B saves Rs. 4,500, ratio = 4:3 ✓

Multiple choice

An amount of Rs. 1275 is distributed among A,B and C in the ratio of 5:7:13. What is the difference between the share of C and B? 1275रूपयों को A,B और C में 5 : 7 :13. के अनुपात में बांट दिया जाता है। तब C और B के भागों में क्या अंतर है?

  1. 331

  2. 306

  3. 316

  4. 126
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total parts = 5+7+13 = 25. Each part = 1275/25 = 51. C's share = 13×51 = 663. B's share = 7×51 = 357. Difference = 663 - 357 = 306. Answer B is correct.

Multiple choice

If the income of A,B and C is in the ratio of 2:5:11 and the income of B is Rs. 297 more than that of A, then the income of C is यदि A,B और C की आय का अनुपात 2 : 5 : 11 हो और B की आय A की आय से 297 रूपये अधिक हो तो C की आय क्या है?

  1. Rs.1908

  2. Rs.1809

  3. Rs. 1890

  4. Rs.1089
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let incomes be 2x, 5x, 11x. Since B - A = 3x = 297, then x = 99. C's income = 11 × 99 = 1089, which matches option D.

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. 24000, find A's income. A और B की आय का अनुपात 2 : 3 है और उनके व्यय का अनुपात 1 : 2 है। यदि उनमें से प्रत्येक की बचत 24000 रू. हो तो A की आय ज्ञात कीजिए।

  1. Rs. 24000

  2. Rs. 72000

  3. Rs. 19200

  4. Rs. 48000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let A's income = 2x and B's income = 3x. Let A's expenditure = y and B's expenditure = 2y (given ratio 1:2). Since both save Rs. 24000, we have: A's saving = 2x - y = 24000, and B's saving = 3x - 2y = 24000. Solving these equations: from first equation y = 2x - 24000, substituting in second: 3x - 2(2x - 24000) = 24000, which gives x = 24000. Therefore A's income = 2x = Rs. 48000.

Multiple choice

A certain amount is divided among A, B and C in the ratio of 3 : 7 : 6 respectively. If the difference between share of A and B is Rs. 2700, what is C's share?

  1. Rs. 4050

  2. Rs. 4000

  3. Rs. 4100

  4. Rs. 4500

  5. Rs. 675
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A, B, C shares are in ratio 3:7:6. Let actual shares be 3x, 7x, 6x. Difference between A and B: 7x - 3x = 4x = 2700, so x = 675. C's share = 6x = 6 × 675 = Rs. 4050. Option B (4000) is close but incorrect.

Multiple choice

The ratio of monthly income of Anuradha and Bani is 3 :5.If income of each is increased by Rs 160, this ratio becomes 25 : 41.What is the Anuradha's monthly income before increment?

  1. Rs.3840

  2. Rs.9000

  3. Rs 2720

  4. Rs 1570

  5. Rs 2570
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let original incomes be 3x and 5x. After increment of 160 each: (3x + 160)/(5x + 160) = 25/41. Cross-multiply: 41(3x + 160) = 25(5x + 160), which gives 123x + 6560 = 125x + 4000, so 2x = 2560, x = 1280. Anuradha's original income = 3 × 1280 = Rs. 3840.

Multiple choice

Cost of diamond varies directly as the square of its weight. A diamond is borken into 4 pieces with their weights in the ratio 1:2:3:4. What is the price of the original diamond if the loss in total value of the diamond amounts to Rs. 140000? किसी हीरे का मूल्य उसके भार के वर्ग के अनुक्रमानुपाती है। एक हीरा चार टुकड़ों में इस प्रकार टूटा कि उसके भारों का अनुपात 1 : 2 : 3 : 4 है। यदि टूटने पर हीरे के मूल्य पर 140000 रू. की हानि हुई हो तो बिना टूटे हीरे का मूल्य कितना था?

  1. Rs. 200000

  2. Rs. 225000

  3. Rs. 215000

  4. Rs. 300000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since cost varies directly as the square of weight, P = k*w². When the diamond breaks into pieces with weight ratio 1:2:3:4, the total weight remains the same. Sum of squares: 1² + 2² + 3² + 4² = 30 parts, while original is (1+2+3+4)² = 100 parts. Loss is (100-30)/100 = 70% of original price. 70% of P = 140000, so P = 200000.

Multiple choice

A precious stone weighing 35 grams worth Rs.12250 is accidently dropped and gets broken into two pieces having weights in the ratio of 2 : 5. If the price varies as the square of the weight. Then find the loss occured. एक मूल्यवान 35 ग्राम का पत्थर, जिसकी कीमत रू.12250 है गिरने के कारण दो भागों में टूट जाता है | जिनके वजन का अनुपात 2: 5 है | यदि इनकी कीमत वजन के वर्ग के अनुक्रमानुपाती हो, तो होने वाली हानि का मान ज्ञात कीजिये |

  1. Rs./रू. 3000

  2. Rs./रू. 4000

  3. Rs./रू. 5000

  4. Rs./रू. 6000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total weight = 35g in ratio 2:5. First piece = (2/7) × 35 = 10g, second piece = (2/7) × 35 = 25g. Price varies as square of weight, so original value k(35)² = 12250, giving k = 10. New value = 10(10² + 25²) = 10(100 + 625) = 7250. Loss = 12250 - 7250 = 5000.

Multiple choice

A, B and C earns total Rs.1450 and spends 60%, 65% and 70% of own’s income respectively. If his savings in the ratio of 14:21:15. Then find the salary of B? A, B एवं C मिलकर कुल रु 1450 कमाते है एवं अपने वेतनों का क्रमशः 60%,65% एवं 70% खर्च करते हैं | यदि उनके द्वारा किये गए बचत का अनुपात 14:21:15 है,तो B का वेतन है |

  1. Rs./रू.450

  2. Rs./रू.500

  3. Rs./रू.600

  4. Rs./रू.750
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A, B, C's savings be 14x, 21x, 15x respectively. If A saves 40% (spends 60%), income = 14x/0.4 = 35x. If B saves 35% (spends 65%), income = 21x/0.35 = 60x. If C saves 30% (spends 70%), income = 15x/0.3 = 50x. Total = 145x = 1450, so x = 10. B's salary = 60x = Rs. 600.

Multiple choice

The ratio of earning of Anuj and Brijesh is 5 : 6. If the earnings of Anuj decreases by 25% and the earnings of Brijesh increases by 20% the new ratio becomes 6 : 11. What is Brijesh's earnings.

  1. Rs. 30000

  2. Rs. 36000

  3. Rs. 33000

  4. Can't be determined

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

Let Anuj = 5x, Brijesh = 6x. After changes: Anuj = 5x × 0.75 = 3.75x, Brijesh = 6x × 1.2 = 7.2x. New ratio 3.75x : 7.2x = 3.75 : 7.2 = 375 : 720 = 25 : 48, not 6 : 11. There's inconsistency in the problem or answer key. However, if we accept the given new ratio of 6:11 is achievable, we can solve: 6x × 0.75 : 6x × 1.2 = 4.5x : 7.2x = 45 : 72 = 5 : 8. Still not 6:11. The problem has contradictory information. Given the answer key says D (Can't be determined), this suggests the information is insufficient or contradictory.