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

Rs.11200 is to be divided among A, B, C and D in such a way that the ratio of share of A : B is 1 : 2, B : C is 3 : 1, C : D is 2 : 3. Find the share of (B + D). रु.11200 को A, B, C और D में इस तरह से बांटा जाता है कि A : B के हिस्से में अनुपात 1 : 2, B : C में अनुपात 3 : 1 और C : D में अनुपात 2 : 3 है | (B +

  1. का हिस्सा ज्ञात कीजिये |

  2. 6000

  3. 7200

  4. 6600

  5. 8000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given A:B = 1:2, B:C = 3:1, C:D = 2:3. Making ratios compatible: A:B = 3:6, B:C = 6:2, C:D = 2:3. Combined: A:B:C:D = 3:6:2:3. Sum = 14 parts. B + D = (6 + 3) parts = 9 parts = (9/14) × 11200 = 7200.

Multiple choice

If in a sale, the discount given on a saree is equal to one-fourth of the marked price and the loss due to this discount is 15%, then the ratio of the cost price to the selling price is- यदि किसी सेल में, साड़ी पर दी गई छूट अंकित मूल्य के एक - चौथाई मूल्य के बराबर है और इस छूट के कारण होने वाली हानि 15% है, तो लागत मूल्य और बिक्री मूल्य का अनुपात है -

  1. 3 : 4

  2. 4 : 3

  3. 10 : 17

  4. 20 : 17
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Discount = 1/4 of marked price, so SP = 3/4 × MP. Loss = 15% means CP = SP/0.85. Let MP = 4x, then SP = 3x and CP = 3x/0.85 = 300x/85 = 60x/17. Ratio CP:SP = 60x/17 : 3x = 60:51 = 20:17.

Multiple choice

The ratio of income of A and B is 2 : 3. The sum of their expenditures is Rs.8000 and the amount of savings of A is equal to amount of expenditure of B. What is the sum of their savings? A और B की आय का अनुपात 2 : 3 है। उनके खर्चों का योग 8000 रू. है और A की बचत की धनराशि B के खर्चे के बराबर है। उनकी बचतों का योग क्या है ?

  1. Rs./रु.4000

  2. Rs./रु.12000

  3. Rs./रु.16000

  4. Rs./रु.22000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let incomes be 2x and 3x. Expenditures are e₁ and e₂ with e₁ + e₂ = 8000. Savings: 2x - e₁ = e₂ (A's savings = B's expenditure). Total savings = (2x - e₁) + (3x - e₂) = 5x - 8000. But e₁ = 2x - e₂, so e₁ + e₂ = 2x = 8000, x = 4000. Total savings = 5(4000) - 8000 = 12000.

Multiple choice

Find two mean proportionals between 2 & 54. 2 और 54 के बीच दो माध्य समानुपातिक ज्ञात कीजिये।

  1. 6 & 18

  2. 6 & 12

  3. 12 & 18

  4. 6 & 9
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For two mean proportionals between 2 and 54, we need to find x and y such that 2:x = x:y = y:54. This means x² = 2y and y² = 54x. From the geometric progression 2, x, y, 54, the common ratio r satisfies 2×r³ = 54, so r³ = 27 and r = 3. Therefore x = 2×3 = 6 and y = 6×3 = 18. The two mean proportionals are 6 and 18.

Multiple choice

The ratio of income of P to that of Q is 5 : 4 and the expenditure of P to that of Q is 3 : 2, if at the end of the year each saves Rs.1600, the income of Q is P की आय का Q की आय से अनुपात 5 : 4 है और P के व्यय का Q के व्यय से अनुपात 3 : 2 है, यदि वर्ष के अंत में प्रत्येक 1600 रु. बचाता है, Q की आय है

  1. Rs./रु.2400

  2. Rs./रु.2800

  3. Rs./रु.3000

  4. Rs./रु.3200
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P's income = 5x and Q's income = 4x. Let P's expenditure = 3y and Q's expenditure = 2y. Savings = Income - Expenditure = 1600 for each. So 5x - 3y = 1600 and 4x - 2y = 1600. From second equation: 2x - y = 800, so y = 2x - 800. Substituting in first: 5x - 3(2x - 800) = 1600, giving 5x - 6x + 2400 = 1600, so -x = -800 and x = 800. Therefore, Q's income = 4x = 4 × 800 = Rs. 3200.

Multiple choice

The ratio of the A.C. and sleeper class fair between two stations 4 : 1 and the ratio between them 3 : 40. If on a perticular days Rs. 1339 are collected from passangers travelling between the two stations, then the amount collected from the A.C. class passengers is - दो स्टेशनों का A.C और स्लीपर के किरायों का अनुपात 4: 1 है और इन से यात्रा करने वाले यात्रियों का अनुपात 3: 40 है यदि किसी दिन इस स्टेशन पर यात्रा करने वाले यात्रियों द्वारा 1339 रू. इकट्ठा होते हैं तो A.C श्रेणी के यात्रियों द्वारा इकट्ठा धन है।

  1. Rs.103

  2. Rs.206

  3. Rs.309

  4. Rs.410
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let AC fare = 4x, Sleeper fare = x. Let AC passengers = 3y, Sleeper passengers = 40y. Total from AC = 4x × 3y = 12xy. Total from Sleeper = x × 40y = 40xy. Total = 52xy = 1339. So xy = 1339/52 = 25.75. Amount from AC = 12xy = 12 × 25.75 ≈ 309. This uses ratio and proportion with two ratios multiplied together.

Multiple choice

If a sum of money is to be divided among Sonu, Vimal, Prashant such that Sonu's share is equal to twice Vimal's share and Vimal's share is 4 times Prashant's share, then their shares are in the ratio. यदि एक धनराशि सोनू, विमल, प्रशान्त के बीच इस प्रकार बांटी जाती है कि सोनू का अंश विमल के अंश के दोगुने के बराबर है और विमल का अंश प्रशान्त के अंश से 4 गुना है, तो उनके अंशों का अनुपात क्या है?

  1. 1 : 2 : 4

  2. 1 : 4 : 1

  3. 8 : 4 : 1

  4. 2 : 4 : 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Prashant's share = x. Then Vimal = 4x, Sonu = 2(4x) = 8x. Ratio Sonu:Vimal:Prashant = 8x:4x:x = 8:4:1.

Multiple choice

price of a precious stone is directly proportional to square of its weight. Due to some reasons a piece of stone is break into three parts in ratio 3:5:2 due to which its total price is reduced by Rs 14260. Find the original price of stone.

  1. 22500 Rs

  2. 23000 Rs

  3. 21500 Rs

  4. 23800 Rs

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

Let original weight = 10x (parts 3:5:2). Original price ∝ (10x)² = 100x². New prices: (3x)² + (5x)² + (2x)² = 9x² + 25x² + 4x² = 38x². Price reduction = 100x² - 38x² = 62x² = 14260. x² = 14260/62 = 230. Original price = 100x² = 100 × 230 = 23000. Matches option B exactly.

Multiple choice

If b is the mean proportional between a and c. Then (a - b)3 : (b - c)3 will be equal to: यदि b, a और c का मध्यानुपाती हो, तो (a - b)3 : (b - c)3 बराबर होगा -

  1. a3/2 : c3/2

  2. b2 : c2

  3. a2 : c2

  4. a3 : c3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If b is mean proportional between a and c, then b^2 = ac. So b = sqrt(ac). Then (a-b)^3 : (b-c)^3 = (a-sqrt(ac))^3 : (sqrt(ac)-c)^3. This simplifies to a^(3/2) : c^(3/2).

Multiple choice

The ratio of monthly income of A, B and C is 2 : 3 : 5. If C’s monthly income is Rs. 120000 more than A’s monthly income , what will be B’s monthly income ?

  1. Rs. 120000

  2. Rs. 144000

  3. Rs. 180000

  4. Rs. 240000

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

Let the incomes be 2x, 3x, and 5x for A, B, and C respectively. C's income exceeds A's by 120000, so 5x - 2x = 120000, giving 3x = 120000 and x = 40000. B's income = 3x = 3 × 40000 = 120000. Option A is correct. Option B (144000) would be 3.6x, C (180000) is 4.5x, and D (240000) equals C's income, not B's.

Multiple choice

A's income is Rs. 140 more than B's income and C's income is Rs. 80 more than D's income. If the ratio of A's and C's income is 2:3 and the ratio of B's and D's income is 1:2, then find the total income of A and C together. 'A' की आय 'B' की आय से 140 रू अधिक है और 'C' की आय 'D' की आय से 80 रू अधिक है। यदि 'A' व 'C' की आय का अनुपात 2 : 3 तथा 'B' व 'D' की आय का अनुपात 1 : 2 है तो A' व 'C की कुल आय ज्ञात कीजिए।

  1. 1000

  2. 780

  3. 860

  4. 770
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Set A = 2x, C = 3x. Using A = B + 140 and B:D = 1:2 (so D = 2B), substitute in C = D + 80 to get 3x = 2B + 80. Since 2x = B + 140, solving gives B = 260, A = 400, C = 600. Total A + C = 1000.

Multiple choice

Ankita has some money, she spends 37.5% of her money on rent, 40% of remaining on food and remaining is divided among her two son Ashu and Aman in ratio 12 : 13. If difference of Ashu and Aman is Rs. 60. Find the amount Ankita hand.

  1. 4000 Rs

  2. 3750 Rs

  3. 4250 Rs

  4. 4800 Rs

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

Let Ankita's total money be x. She spends 37.5% on rent, so remaining = 62.5% of x = 5x/8. She then spends 40% of remaining on food: 40% of 5x/8 = x/4. Money left for sons = 5x/8 - x/4 = 3x/8. This is divided in ratio 12:13, so difference = (13-12)/(12+13) × 3x/8 = 3x/200 = 60. Thus x = Rs. 4000.

Multiple choice

A sum is divided among P,Q,R and S such that the ratio between P and Q is 3:5, Q and R is 6:7 and R and S is 8:9. What is the ratio of money between P and S. एक धन P,Q,R और S में एक प्रकार बाँटा गया कि P और Q में अनुपात 3 : 5 है, Q और R में अनुपात 6 : 7 और R और S में अनुपात 8 : 9 है। P और S को प्राप्त होने वाले भागों का अनुपात है-

  1. 36:35

  2. 16:35

  3. 33:37

  4. 19:21
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find P:S, we need to align the ratios: P:Q = 3:5 = 18:30, Q:R = 6:7 = 30:35, R:S = 8:9. Now P:Q:R = 18:30:35. For R:S = 8:9, if R = 35, we need to scale so 8k = 35, giving k = 35/8. Then S = 9k = 9(35/8) = 315/8. So P:S = 18:(315/8) = 144:315 = 16:35.

Multiple choice

An amount of money is to be divided among A, B and C in the ratio 5:11:23 respectively. If the difference between the total share of A and B together and C's share is Rs.2800. What is the difference between B and C's share? एक धनराशि A, B और C में क्रमशः 5 : 11 : 23 के अनुपात में बाँटी जाती है। यदि A और B के कुल भाग को मिलाकर और C के भाग का अन्तर 2800 रू. है तो B और C के भाग में क्या अन्तर है?

  1. Rs.3680

  2. Rs.4800

  3. Rs.4600

  4. Rs.5200
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let amounts be 5x, 11x, 23x. Given: difference between (A + B) and C is 2800. So |(5x + 11x) - 23x| = 2800 → |16x - 23x| = 2800 → 7x = 2800 → x = 400. We need B - C = |11x - 23x| = |11x - 23x| = 12x = 12 × 400 = 4800. Note: C has the largest share (23 > 16), so C > (A + B).