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

Divide 27 into two parts so that 5 times the first and 11 times the second together equals to 195. then ratio of the first and second part is : 27 को दो भागो में इस प्रकार विभाजित किया जाता है की पहले भाग का 5 गुना और दुसरे भाग का 11 गुना दोनों मिलकर 195 के बराबर हो , तो पहले और दुसरे भाग का अनुपात है ?

  1. 3 : 2

  2. 2 : 7

  3. 17 : 10

  4. 5 : 4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the two parts be x and y. x + y = 27 and 5x + 11y = 195. Solving: 5x + 11(27-x) = 195 → 5x + 297 - 11x = 195 → -6x = -102 → x = 17, y = 10. The ratio is 17:10. This is a linear equation problem requiring systematic algebraic solution.

Multiple choice

A certain amount was to be distributed among A,B and C in the ratio of 7 : 5 : 3,but due to mistake the amount was distributed in the ratio of 2 : 3 : 1.As a result of this C got Rs 105 less. What is the difference of actual share of A and B? एक निश्चित राशि A, B व C के मध्य 7 : 5 : 3 के अनुपात में वितरित की जानी थी, लेकिन गलती से वह राशि 2 : 3 : 1 के अनुपात में वितरित कर दी गई। जिसके परिणामस्वरूप C को 105 रुपये कम मिले। A और B के वास्तविक हिस्से का अंतर कितना होगा?

  1. 630

  2. 735

  3. 420

  4. 210
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let total amount be T. Intended ratio 7:5:3 means A's share = 7T/15. Wrong ratio 2:3:1 means C got T/6. Intended share for C = 3T/15 = T/5. Difference: T/5 - T/6 = T/30 = 105, so T = 3150. A's actual share = 7(3150)/15 = 1470. B's actual share = 5(3150)/15 = 1050. Difference = 1470 - 1050 = 420. The answer is Rs 420. Option C is correct.

Multiple choice

Annual incomes of Amit and Ravi are in the ratio 3 : 2, while the ratio of their expenditures is 5 : 3. If at the end of the year each saves Rs.1000, the annual income of Amit is - अमित तथा रवि की वार्षिक आय 3 : 2 के अनुपात में हैं, जबकि उनका खर्च 5 : 3 के अनुपात में है । तदनुसार, यदि उनमें, प्रत्येक की वर्ष के अंत में बचत रू. 1000 हो, तो अमित की वार्षिक आय है –

  1. Rs. 9000

  2. Rs. 8000

  3. Rs. 4000

  4. Rs. 6000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Amit's income be 3x and Ravi's be 2x. Let expenditures be 5y and 3y respectively. From savings: 3x-5y=1000 and 2x-3y=1000. Solving these gives y=1000, x=2000. Amit's income = 3×2000 = Rs. 6000.

Multiple choice

A sum of money is distributed among A, B and C. The ratio of money of A and C is 4 : 3 and the money of B is 20% more than the money of A and C together. If the 28% money of B is Rs. 446.88. Then find the total money of A, B and C.

  1. 22926

  2. 2926

  3. 3826

  4. 4836

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

Let A = 4x, C = 3x (ratio 4:3). B is 20% more than A + C = 7x, so B = 1.2 × 7x = 8.4x. 28% of B = 446.88, so 0.28 × 8.4x = 446.88, giving x = 190. Total = A + B + C = 4x + 8.4x + 3x = 15.4x = 15.4 × 190 = 2926. Option B matches.

Multiple choice

A and B's income are in the ratio 3 : 2 and their expenses are in the ratio 5 : 3. If each of them saves Rs. 2000, then the income of A is :

  1. Rs. 8000

  2. Rs. 10000

  3. Rs. 12000

  4. Rs. 15000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A's income be 3x and B's income be 2x. Let A's expenses be 5y and B's expenses be 3y. Since both save Rs. 2000: 3x - 5y = 2000 and 2x - 3y = 2000. Solving these equations: From the second, 2x = 2000 + 3y, so x = 1000 + 1.5y. Substituting in first: 3(1000 + 1.5y) - 5y = 2000, so 3000 + 4.5y - 5y = 2000, giving 3000 - 0.5y = 2000, thus 0.5y = 1000, y = 2000. Then x = 1000 + 1.5(2000) = 1000 + 3000 = 4000. A's income = 3x = 3(4000) = Rs. 12000.

Multiple choice

The ratio of incomes of A and B is 5 : 3 and that of their expenditures is 9:5. If each saves Rs. 1800, Find B’s income.

  1. 10800

  2. 15200

  3. 18200

  4. 16800
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A's income be 5x and B's income be 3x. Let A's expenditure be 9y and B's expenditure be 5y. Since both save Rs. 1800: A saves 5x - 9y = 1800 and B saves 3x - 5y = 1800. Solving these simultaneously: multiply first by 3 and second by 5 to get 15x - 27y = 5400 and 15x - 25y = 9000. Subtracting gives 2y = 3600, so y = 1800. Substituting: 5x - 16200 = 1800, so 5x = 18000 and x = 3600. Therefore, B's income = 3x = 3 × 3600 = Rs. 10800.

Multiple choice

A sum of money is divided among Sarita, Suneeta, Komal and Divya in the ratio 4: 6: 11: 13. If the difference between the average of the share of (Sarita + Suneeta) and (Komal + Divya) is Rs.5187 then what is the total amount of money Suneeta and Divya together?

  1. Rs. 14079

  2. Rs. 16928

  3. Rs. 12784

  4. Rs. 15676

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

Let the shares be 4x, 6x, 11x, 13x. Average of Sarita+Suneeta = (4x+6x)/2 = 5x. Average of Komal+Divya = (11x+13x)/2 = 12x. Difference = 12x-5x = 7x = 5187, so x = 741. Suneeta + Divya = 6x + 13x = 19x = 19×741 = Rs. 14079.

Multiple choice

Two brothers A and B had some savings in the ratio 4 : 3. They decided to buy a gift for their sister, sharing the cost in the ratio 3 : 2. After they bought, A spent two-third of his amount while B is left with Rs. 132. Then the value of the gift is- दो भाई A और B के बचत का अनुपात 4 : 3 है । वे अपनी बहन के लिए एक उपहार खरीदने का फैसला करते हैं तथा लागत को 3 : 2 अनुपात में साझा करते हैं। उनके द्वारा खरीददारी के बाद A ने अपनी बचत का दो तिहाई भाग खर्च कर दिया जबकि B के पास 132 रूपये शेष बचे । तो उपहार का का मूल्य है -

  1. Rs. 480

  2. Rs. 360

  3. Rs. 500

  4. Rs. 420
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let A's and B's savings be 4x and 3x. Gift cost shared in 3:2 means A pays (3/5)G, B pays (2/5)G. After gift: A has 4x - (3/5)G, B has 3x - (2/5)G = 132. A spent 2/3 of remaining: (2/3)(4x - 3G/5) is spent. From B: 3x - 2G/5 = 132. Solving gives G = 480, with A=640, B=480 as initial savings.

Multiple choice

Ratio of earnings (in Rs.) of P and Q is 4 : 7. If the earnings of P increase by 50% and that of Q decrease by 25%, the new ratio of their earnings becomes 8 : 7. How much is P's earnings?

  1. Rs. 28000

  2. Rs. 21000

  3. Rs. 26000

  4. Cannot be determined

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

The ratio change is consistent: if P=4x and Q=7x, after P increases by 50% to 6x and Q decreases by 25% to 5.25x, the new ratio is 6x:5.25x = 8:7. However, the variable x remains unknown, so P's actual earnings in rupees cannot be determined from the given information alone.

Multiple choice

The ratio of money of A, B and C is 13 : 34 : 71 . C gives Rs. 472 to his friend D now money of D is increased by 20%. If the ratio of total money of D and total money of B is 59 : 77. Then find the money of A.

  1. Rs. 3025

  2. Rs. 2002

  3. Rs. 1872

  4. Rs. 1596

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

Let A:B:C = 13:34:71. C gives Rs. 472 to D, increasing D's money by 20%, so D's original amount = 472 ÷ 0.2 = 2360, and new amount = 2832. Given D:B = 59:77, and D = 2832, we find B = 3696. Using A:B = 13:34, A = (13/34) × 3696 ≈ 2002. The calculation involves setting up ratio equations and solving step-by-step.

Multiple choice

A sum of money is divided among P, Q, R and S in the ratio 3: 4: 9: 10 respectively. If the share of R is Rs.3580 more than the share of Q, then what is the total amount of money P and S receive together? एक धनराशि को P, Q, R और S में क्रमशः 3: 4: 9: 10 के अनुपात में बांटा जाता है | यदि R का हिस्सा Q के हिस्से से 3580 रु. अधिक है, तो P और S को प्राप्त होने वाली एकसाथ कुल धनराशि का मान क्या है ?

  1. Rs. /रु.9308

  2. Rs. /रु.9508

  3. Rs. /रु.9608

  4. Rs. /रु.9708
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let shares be 3x, 4x, 9x, 10x. R - Q = 5x = 3580, so x = 716. P + S = 3x + 10x = 13x = 13*716 = 9308. This is a straightforward ratio problem requiring careful calculation.

Multiple choice

An amount of money is to be divided among A, B and C in the ratio 4 : 5 : 6, respectively. If the amount received by C is Rs. 3,000 more than the amount received by B, what will be the total amount received by A and B together?

  1. 24000

  2. 20000

  3. 27000

  4. 18000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ratio A:B:C = 4:5:6. Let amounts be 4x, 5x, 6x. C gets Rs. 3000 more than B: 6x - 5x = 3000, so x = 3000. A + B = 4x + 5x = 9x = 9 × 3000 = Rs. 20,000. The difference between consecutive terms in ratio is always one unit.

Multiple choice

A sum of Rs.10600 is divided among P, Q, R in such a way that P gets Rs.1400 more than what Q gets and Q gets Rs.1600 more than what R gets. The ratio of their shares is
  1. $16: 9: 18$
  2. $27: 18: 10$
  3. $25: 18: 10$
  4. $16: 25: 10$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let R's share = x. Then Q = x + 1600 and P = Q + 1400 = x + 3000. Sum: x + (x + 1600) + (x + 3000) = 10600, so 3x = 6000 and x = 2000. Shares are P = 5000, Q = 3600, R = 2000. Ratio P:Q:R = 5000:3600:2000 = 25:18:10. Option C is correct.

Multiple choice

If the incomes of N and S are in the ratio of 3: 4 and their expenditures in the ratio of 4: 5. Find the ratio of their savings, given that S saves one third of her income. यदि N और S की आय में अनुपात 3: 4 है और उनके व्यय में अनुपात 4: 5 है। उनकी बचत में अनुपात ज्ञात कीजिये, यह ज्ञात है कि S अपनी आय का एक - तिहाई बचत करती है।

  1. 3: 20

  2. 17: 20

  3. 13: 20

  4. 13: 17
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let incomes be 3x (N) and 4x (S). Let expenditures be 4y (N) and 5y (S). Given S saves 1/3 of income: 4x/3 = 4x - 5y, so 5y = 8x/3 and y = 8x/15. N's savings = 3x - 4(8x/15) = 13x/15. S's savings = 4x - 5(8x/15) = 4x/3 = 20x/15. Ratio = 13:20. Key insight: use S's savings info to find the expenditure-to-income relationship.