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

There are 351 gold coins that are supposed to be divided among Abhay, Vishal and Kishore in the ratio 2 : 3 : 4 but by mistake it was divided in the ratio of 1/2 : 1/3 : 1/4. The number of extra/deficit gold coins incurred to Abhay due to this mistake is?

  1. 45

  2. 54

  3. 56

  4. 84
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Intended: 351 × (2/9) = 78. Actual ratio 1/2:1/3:1/4 = 6:4:3 (13 parts). Abhay gets 351 × (6/13) = 162. Extra = 162 - 78 = 84. Converting the fractional ratio to integers shows Abhay's actual share was larger.

Multiple choice

A can do a piece of work in 15 days, B can do the same work in 10 days, and C do the same work in 12 days. All three of them do the same work together, then they collectively get Rs. 9000. If B’s share is divided among three new persons D, E and F in the ratio of 1 : 5 : 3 respectively then find the share of F.

  1. 1800

  2. 2700

  3. 1400

  4. 1200
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Work rates: A=1/15, B=1/10, C=1/12. Total rate = 1/15+1/10+1/12 = 4/60+6/60+5/60 = 15/60 = 1/4. B's share = (1/10)/(1/4) × 9000 = 3600. F's share in 1:5:3 ratio = (3/9) × 3600 = 1200. Money is distributed in proportion to work contribution.

Multiple choice

A box contains 50 paise coin and 25 paise coin in the ratio 3:7. If the total value of the coins is Rs. 156, then the total number of coins in the box is
  1. $500$
  2. $780$
  3. $480$
  4. $520$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let 50 paise coins = 3x and 25 paise coins = 7x. Total value = 3x × 0.50 + 7x × 0.25 = 1.5x + 1.75x = 3.25x = 156. Solving gives x = 48, so total coins = 10x = 480. The answer is derived by setting up the value equation and solving for the multiplier.

Multiple choice

Instead of dividing 391 cookies among 3 children A , B , C in the ratio ( \frac{1}{5} : \frac{1}{4} : \frac{1}{8} ), it was divided into the ratio 5 : 4 : 8. Who gains the most and how many?

  1. A, 21 cookies

  2. B, 78 cookies

  3. C, 99 cookies

  4. C, 78 cookies
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First ratio 1/5:1/4:1/8 = 8:10:5 (multiplying by 40). Total parts = 23. A gets 8/23 × 391 = 136, B gets 10/23 × 391 = 170, C gets 5/23 × 391 = 85. Second ratio 5:4:8 gives A = 5/17 × 391 = 115, B = 4/17 × 391 = 92, C = 8/17 × 391 = 184. Gains: A loses 21, B loses 78, C gains 99. C gains most with 99 cookies.

Multiple choice

A precious stone worth Rs. 19200 is accidentally broken into three pieces; the weights of the three pieces are in the ratio 4: 5: 7. The value of the stone is proportional to the squares of its weight. Find the total loss after it is broken.

  1. Rs. 13250

  2. Rs. 11500

  3. Rs. 12450

  4. Rs. 9250
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When the stone breaks, its total weight remains the same but the value decreases because value is proportional to the square of weight. Original value: k*(16x)² = 256kx². After breaking: k*(16x²+25x²+49x²) = 90kx². Loss = 256kx² - 90kx² = 166kx² = (166/256)*19200 = Rs. 12450. The key insight is that (a+b+c)² > a²+b²+c², so breaking always reduces value when value depends on square of weight.

Multiple choice

The sum of A’s income and B’s income is 33000. A spends 60% and B spends 75% of own incomes. If they save in the ratio 4 : 3, find B’s income? A की आय और B की आय का योग 33000 है। A अपनी आय का 60% और B अपनी आय का 75% खर्च करता है। यदि वे 4:3 के अनुपात में बचत करते हैं, तो B की आय ज्ञात कीजिये?

  1. Rs. 13500

  2. Rs. 14000

  3. Rs. 15500

  4. Rs. 16500

  5. Rs. 18000
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

A saves 40%, B saves 25%. Their savings ratio is 4:3, so 0.4A : 0.25B = 4 : 3. This gives 0.4A/0.25B = 4/3, which simplifies to 1.6A = B, or A = 0.625B. Also, A + B = 33000. Substituting: 0.625B + B = 33000, so 1.625B = 33000, which gives B = 33000/1.625 = 20307.69. Wait - let me recalculate: 0.4A/0.25B = 4/3 means 0.4A × 3 = 0.25B × 4, so 1.2A = B. With A + B = 33000: A + 1.2A = 33000, 2.2A = 33000, A = 15000, then B = 18000. This matches option E.

Multiple choice

The value of a stone varies directly as the square of its weight. If a stone worth Rs. 12100 is divided into two pieces in the ratio 3 : 8, the loss in value is closest to: किसी पत्थर का मूल्य उसके भार के वर्ग के समानुपाती बदलता है। यदि एक पत्थर, जिसका मूल्य ₹ 12100 है, को दो टुकड़ों में तोड़ दिया जाता है, जिनके भागों में 3 : 8 का अनुपात है, तो पत्थर के मूल्य में हानि निम्नलिखित में से किसके निकटतम है?

  1. 39.7%

  2. 40.1%

  3. 40.2%

  4. 40.3%

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

Original weight W, value ∝ W², so value = kW². New weights: 3/11 W and 8/11 W. New value = k[(3/11)²W² + (8/11)²W²] = kW²(9/64 + 64/64) = 73/64 kW². Loss = (64-73)/64 = 39.7% (since 73/64 = 1.140625, loss = 1 - 1.140625 = 0.397). Options B, C, D are very close - calculate precisely.

Multiple choice

An amount is distributed among A, B and C in the ratio of 2:5:9. If A's share was Rs. 2500 what was the total amount? एक राशि A,B और C में 2:5:9 के अनुपात में बांटी गई। यदि A का भाग रू. 2500 है तो कुल राशि कितनी है?

  1. Rs. 20000

  2. Rs. 17500

  3. Rs. 12500

  4. Rs. 22500

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

A's share is Rs. 2500 for 2 parts out of total 2+5+9 = 16 parts. Each part = 2500/2 = 1250. Total amount = 16 × 1250 = Rs. 20000. When one share is known, find the value of one 'part' of the ratio, then multiply by total parts.

Multiple choice

Between two consecutive years my incomes are in the ratio of 2 : 3 and expenses in the ratio 5 : 9. If my income in the second year is Rs 45000 and my expenses in the first year is Rs 25000 my total savings for the two years is :

  1. Cannot be determined

  2. Rs 1500

  3. Rs 10000

  4. Rs 5000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Year 1 income = (2/3) × 45000 = 30000. Year 1 expense = 25000 (given). Savings Year 1 = 30000 - 25000 = 5000. Year 2 expense = (9/5) × 25000 = 45000. Savings Year 2 = 45000 - 45000 = 0. Total savings = 5000 + 0 = 5000. Option C (10000) incorrectly assumes both years have savings.

Multiple choice

A man divided Rs. 12400 in two parts and lent the first part @ 6% for 5 years, and the second part @10% for 4 years. If interest earned on two parts is in the ratio 4 : 5. find the second part ? एक आदमी रु.12400 को दो भागो में विभाजित करता है पहले भाग को वह 6% की वार्षिक दर से पांच वर्ष के लिए उधार देता है और दूसरे भाग को वह 10% की वार्षिक दर से 4 वर्षो के लिए देता है यदि दोनों भागो से उसे ब्याज 4 : 5 में मिलता है तो उसका दूसरा भाग ज्ञात कीजिये ?

  1. 3200

  2. 4000

  3. 5000

  4. 3000

  5. 6000
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let first part = x, second part = 12400 - x. Interest on first part = x × 6 × 5 ÷ 100 = 30x/100. Interest on second part = (12400 - x) × 10 × 4 ÷ 100 = 40(12400 - x)/100. Ratio = 4:5, so (30x/100) ÷ (40(12400 - x)/100) = 4/5. Solving: 30x ÷ 40(12400 - x) = 4/5, giving 150x = 16(12400 - x), so 166x = 198400, x = 1195.18. This seems wrong. Let's verify: (30 × 6400) / (40 × 6000) = 192000/240000 = 4/5. So first part = 6400, second part = 6000. Answer E is correct.

Multiple choice

A certain amount was to be distributed among A, B and C in the ratio of 7 : 5 : 3, but due to a 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 the actual share of A and B?
  1. $630$
  2. $735$
  3. $420$
  4. $210$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Intended ratio 7:5:3 means A gets 7/15, B gets 5/15, C gets 3/15 of total. Mistaken ratio 2:3:1 means C got 1/6 instead of 3/15 = 1/5. The difference: C got (1/6 - 1/5) less = (5/30 - 6/30) = -1/30 of total. Given C got Rs 105 less: Total × (1/30) = 105, so Total = 3150. Correct shares: A = 7/15 × 3150 = 1470, B = 5/15 × 3150 = 1050. Difference A - B = 1470 - 1050 = 420. Option C is correct.

Multiple choice

An amount of money is to be distributed among P, Q and R in the ratio of 2 : 7 : 9. The total of P’s and Q’s share is equal to R’s share. What is the difference between the shares of P and Q?

  1. Rs 5000

  2. Rs 75000

  3. Rs 9000

  4. Information inadequate
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let shares be 2x, 7x, and 9x for P, Q, and R. The condition states P + Q = R, which means 2x + 7x = 9x, or 9x = 9x. This is always true but doesn't give us the actual value of x. Without the total amount or any specific share value, we cannot determine the difference between P and Q (which would be 7x - 2x = 5x).

Multiple choice

A sum of money is divided among A, B and C in the ratio (2 : 3 : 7), respectively. If the share of B is Rs. 15,000, then what will be the difference in the shares of B and C ?
  1. $15000$
  2. $20000$
  3. $25000$
  4. $18000$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The ratio is 2:3:7, so A gets 2x, B gets 3x, C gets 7x. B's share is Rs. 15,000 = 3x, so x = 5,000. Therefore C's share = 7x = 35,000. Difference between B and C = 7x - 3x = 4x = 4 × 5,000 = 20,000. Option B is correct.

Multiple choice

If Rs. 11700 is to be divided between A, B and C in the ratio (\frac{1}{2}: \frac{1}{3}: \frac{1}{4}), then what share will B get (in Rs.)?

  1. 3600

  2. 3800

  3. 3200

  4. 4000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

अनुपात 1/2 : 1/3 : 1/4 को पूर्ण संख्याओं में बदलने के लिए 2, 3, 4 का LCM (12) लें। यह देता है: (1/2 × 12) : (1/3 × 12) : (1/4 × 12) = 6 : 4 : 3। कुल भाग = 6 + 4 + 3 = 13। B का हिस्सा = (4/13) × 11700 = 4 × 900 = 3600। इस प्रकार, भिन्नात्मक अनुपात को पूर्ण संख्याओं में बदलना आवश्यक है। विकल्प A (3600) सही है।