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

In a bag, there are coins of 5ps, 10ps and 25ps in the ratio of 3:2:1. If there are Rs. 60 in all, how many 5ps coins are there?

  1. 100

  2. 200

  3. 300

  4. 400
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the number of coins be 3x (5ps), 2x (10ps), and x (25ps). Total value = (3x × 0.05) + (2x × 0.10) + (x × 0.25) = 0.15x + 0.20x + 0.25x = 0.60x = Rs. 60. Solving: x = 60/0.60 = 100. Therefore, number of 5ps coins = 3x = 300. Option C is correct. Quick check: 300×5ps=Rs.15, 200×10ps=Rs.20, 100×25ps=Rs.25; Total=Rs.60 ✓

Multiple choice

The monthly income of P and Q are Rs 40000 and Rs 50000. The monthly expenditure of P is Rs 16000. If the ratio of monthly expenditure of P and Q is 2:3, then what is the sum of their monthly savings?

  1. Rs 40000

  2. Rs 42000

  3. Rs 48000

  4. Rs 50000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

P saves Rs 40000 - Rs 16000 = Rs 24000. Since the expenditure ratio is 2:3, Q's expenditure is (3/2) × 16000 = Rs 24000, so Q saves Rs 50000 - Rs 24000 = Rs 26000. Total savings = 24000 + 26000 = Rs 50000.

Multiple choice

Rs. 8500 is to be divided amongst 5 men, 6 women and 8 boys in such way each man, each woman, and each boy share are in the ratio of 10: 7: 1. What is the share of one woman? रू. 8500 की एक राशि 5 पुरूषों, 6 महिलाओं और 8 लड़कों में इसप्रकार बॉटा जाता है कि प्रत्येक पुरूष, प्रत्येक महिला एवं प्रत्येक लड़के के भाग का अनुपात 10 : 7 : 1 है। एक महिला का हिस्सा क्या होगा?

  1. Rs. 85 85 रू.

  2. Rs. 385 385 रू.

  3. Rs. 850 850 रू.

  4. Rs. 595 595 रू.

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

Total ratio units: 5×10 + 6×7 + 8×1 = 50 + 42 + 8 = 100. Women's share is 42 units out of 100. Each woman gets 8500 × 42/100 ÷ 6 = Rs. 595.

Multiple choice

3425 is to be divided among X, Y and Z in such a way that if X share reduced by 55, Y share reduced by Rs 40 and Z share increased by 45 then rest of the amount distributed among them in ratio 4:5:6. find the share of X.

  1. 988

  2. 955

  3. 961

  4. 965

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

Let original shares be X, Y, Z. After modifications: X-55, Y-40, Z+45 are distributed in ratio 4:5:6. Total after modifications = 3425-55-40+45 = 3375. If new amounts are 4k, 5k, 6k, then 15k = 3375, k = 225. So new amounts: 900, 1125, 1350. Original shares: X=900+55=955, Y=1125+40=1165, Z=1350-45=1305. Check: 955+1165+1305=3425. ✓

Multiple choice

There are total 100 coins consisting of 20 paise, 50 paise and Rs 1 in the ratio of 7 : 8 : 5. What is the number of coins of 50 paise if the difference between the amount yielded by 20 paise and Rs 1 coin is 18?

  1. 32

  2. 40

  3. 56

  4. 64

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

Ratio 7:8:5, total parts = 20. Number of coins: 20p = 7×5=35, 50p = 8×5=40, Rs1 = 5×5=25. Amounts: 20p coins = 35×0.20 = Rs7, Rs1 coins = 25×1 = Rs25. Difference = 25-7 = Rs18. This matches the given condition. 50 paise coins = 40.

Multiple choice

A certain amount was to be distributed among A, B and C in the ratio 2 :3 :4 respectively, but was erroneously distributed in the ratio 7:2:5 respectively. As a result of this, B got Rs 40 less. What is the amount? एक निश्चित राशि को क्रमशः 2 : 3 : 4 के अनुपात में A, B और C के बीच वितरित किया जाना था, लेकिन गलती से क्रमशः 7: 2: 5 के अनुपात में वितरित किया गया था। इसके परिणामस्वरूप, B को 40 रुपये कम मिले। राशि क्या है?

  1. 270

  2. 280

  3. 210

  4. 230

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

Correct ratio is 2:3:4 (total 9 parts). B should get 3/9 = 1/3 of amount. Incorrect ratio is 7:2:5 (total 14 parts). B actually got 2/14 = 1/7 of amount. Difference = 1/3 - 1/7 = 4/21 of amount = Rs 40. So amount = 40 × 21/4 = Rs 210.

Multiple choice

A sum is divided among A,B,C and D such that the ratio of the shares of A and B is 3:5, that of B and C is 2:3 and that of C and D is 5:7. If the difference between the shares of C and A is Rs. 5580 , then the sum (in Rs.) of the shares of B and D is:

  1. 18840

  2. 21400

  3. 19220

  4. 17980
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First, combine the ratios to get A:B:C:D = 6:10:15:21. Let the shares be 6k, 10k, 15k, 21k. Given C - A = 15k - 6k = 9k = 5580, so k = 620. Therefore B + D = 10k + 21k = 31k = 31 × 620 = 19220. Option A (18840) would result from incorrect ratio combination, while Option D (17980) uses an arithmetic error in the final step.

Multiple choice

A, B and C spend 80%, 85% and 75% of their incomes, respectively. If their savings are in the ratio 8:9:20 and the difference between the incomes of A and C is Rs. 18,000, then the income of B is:

  1. Rs. 24,000

  2. Rs. 27,000

  3. Rs. 30,000

  4. Rs. 36,000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Savings ratio is 8:9:20. Savings are 20%, 15%, 25% of incomes. So incomes ratio = (8/20):(9/15):(20/25) = 0.4:0.6:0.8 = 2:3:4. Let incomes be 2x, 3x, 4x. Difference between C and A = 2x = 18,000. Thus x = 9,000. B's income = 3x = 27,000.

Multiple choice

A bag contains 50 p, 25 p, and 20 p coins in the ratio 10 : 8 : 5, amounting to Rs. 240. Find the number of coins of each type respectively.

  1. 280, 220, 160

  2. 300, 240, 150

  3. 320, 250, 180

  4. 280, 200, 120
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let coins be 10x, 8x, 5x. Total value: 10x(0.50) + 8x(0.25) + 5x(0.20) = 5x + 2x + x = 8x = 240. So x = 30. Therefore: 50p coins = 10 × 30 = 300; 25p coins = 8 × 30 = 240; 20p coins = 5 × 30 = 150. Check: 300(0.50) + 240(0.25) + 150(0.20) = 150 + 60 + 30 = 240.

Multiple choice

A sum of Rs. x is divided among A , B and C such that the ratio of shares of A and B is 7 : 12 and that of B and C is 8 : 5. If the difference in the shares of A and C is Rs. 214 , then the value of x is : x रुपये की राशि को A, B और C में इस प्रकार विभाजित किया जाता है कि A और B के शेयरों का अनुपात 7:12 है और B और C के शेयरों का अनुपात 8:5 है। यदि A और C के शेयरों में अंतर रु. 214 है, तो x का मान है:

  1. 11556

  2. 11128

  3. 11770

  4. 11342

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

A:B = 7:12 and B:C = 8:5. To combine, make B equal: LCM of 12 and 8 is 24. A:B = 14:24, B:C = 24:15. So A:B:C = 14:24:15. Let shares be 14k, 24k, 15k. Difference between A and C: |14k - 15k| = k = 214. Total x = 14k + 24k + 15k = 53k = 53 × 214 = 11342.

Multiple choice

Pankaj invests an amount after dividing in three different schemes A, B and C giving the interest at the rate of 10%, 12% and 15% respectively and the accumulated interest for one year is Rs. 3200. The amounts invested in A, B and C are in the ratio of 8 : 5 : 12. What amount did he invest in scheme B ? पंकज तीन अलग-अलग योजनाओं A, B और C में क्रमशः 10%, 12% और 15% की दर से ब्याज देने के बाद एक राशि का निवेश करता है और एक वर्ष के लिए संचित ब्याज रु 3200 है A, B और C में निवेश की गई राशि 8: 5: 12 के अनुपात में है। उसने योजना B में कितनी राशि का निवेश किया?

  1. 5600

  2. 4500

  3. 5000

  4. 4000

  5. 5500
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let amounts be 8x, 5x, 12x for schemes A, B, C respectively. Interest: 0.1×8x + 0.12×5x + 0.15×12x = 3200. Simplifying: 0.8x + 0.6x + 1.8x = 3200, so 3.2x = 3200, giving x = 1000. Amount in B = 5x = 5000. Option A (5600) would be if x = 1120. Option D (4000) would be if x = 800.

Multiple choice

A sum of Rs. 12000 is divided between A, B, C, and D such that the ratio of shares of A and B is (8 : 9), that of B and C is (2 : 3) and that of C and D is (9 : 13). What is the difference between the shares of B and D?

  1. 2760

  2. 2520

  3. 2400

  4. 1320
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Chain the ratios: A:B = 8:9, B:C = 2:3, C:D = 9:13. Convert to common terms: A:B = 8:9 = 16:18, B:C = 2:3 = 18:27, C:D = 9:13 = 27:39. So A:B:C:D = 16:18:27:39. Total parts = 16+18+27+39 = 100. Each part = 12000/100 = 120. D - B = 39×120 - 18×120 = 21×120 = 2520.

Multiple choice

Amit invested an amount into two parts in the ratio of 4 : 3 on compound interest for two years at the rates of 20% & 15% respectively. If he exchanges rate of interests, then he will get Rs. 705 less interest than earlier interest, then find how much Simple interest he will get, if he invests total amount at the rate of 10 % for two years?

  1. 14700

  2. 8400

  3. 7800

  4. 44000

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

Let parts be 4x and 3x. At 20% and 15% CI for 2 years: Interest1 = 4x(1.2²-1) = 4x(0.44) = 1.76x. Interest2 = 3x(1.15²-1) = 3x(0.3225) = 0.9675x. Total = 2.7275x. If swapped: Interest1' = 4x(1.15²-1) = 4x(0.3225) = 1.29x. Interest2' = 3x(1.2²-1) = 3x(0.44) = 1.32x. Total' = 2.61x. Difference: 2.7275x - 2.61x = 0.1175x = 705. So x = 705/0.1175 = 6000. Total = 7x = 42000. SI at 10% for 2 years = 42000×10%×2 = 8400.