Quantitative Aptitude

Mixtures and Alligation

1,816 Questions
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Mixtures and Alligation Questions

Multiple choice

A vessel is filled with milk. Three liters of milk is drawn from it and replaced with water. Again 3 liters are drawn and replaced with water. The ratio of milk and water is now found to be 4 : 5. What is the capacity of the vessel in liters? एक पात्र दूध से भरा हुआ है | तीन लीटर दूध निकाला जाता है और पानी से प्रतिस्थापित किया जाता है | पुनः 3 लीटर निकाला जाता है और पानी से प्रतिस्थापित किया जाता है। अब दूध और पानी का अनुपात 4 : 5 प्राप्त किया जाता है | पात्र की क्षमता लीटर में क्या है?

  1. 9

  2. 12

  3. 3

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

Let capacity = x liters. After first replacement: milk = x-3. After second: milk = (x-3)²/x. Final milk ratio = 4/9, so (x-3)²/x² = 4/9. Solving: 3(x-3) = 2x, giving x = 9. Verification: after two operations, milk fraction = (6/9)² = 36/81 = 4/9 ✓

Multiple choice

3 containers A, B and C contain water, milk and acid respectively in equal quantities. 10% of the content of A is taken out and poured to B. Then same percentage from B is transferred to C, from which again the same percentage is transferred to A. Find the percentage of milk in container A at the end of the process.

  1. 0.88%

  2. 0.75%

  3. 0.98%

  4. 0.90%

  5. cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Track the milk through each transfer: initially A has 100 water, B has 100 milk. After 10% of A (10 water) moves to B, B has 110 total (100 milk + 10 water). When 10% of B (11 units) moves to C, it contains 10 milk and 1 water. Finally, 10% of C (11.1 units) moves back to A. The milk reaching A is 11 × 10/111 = 0.99 units out of A's final 101.1 units, giving 0.98%. This successive percentage problem requires tracking composition changes at each step.

Multiple choice

Ram purchased two different kinds of alcohol. In the first mixture the ratio of alcohol to water is 3 : 4 . and in the second mixture it is 5 : 6. If he mixes the two given mixtures and makes a third mixture of 36 litre in which the ratio of alcohol to water is 4 : 5, find the quantity of the first mixture that is required to make 36 litre of the third kind of mixture is :

  1. 6

  2. 7

  3. 14

  4. 9

  5. 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x liters from first mixture (3:7 alcohol:water) and (36-x) from second (5:11 alcohol:water). Total alcohol = 3x/7 + 5(36-x)/11 = 36 × 4/9 = 16. Solving 33x + 180(36-x) = 1232 gives 33x - 180x = 1232 - 6480, so x = 14 liters.

Multiple choice

A can contains a mixture of two liquids A and B in the ratio 6 : 11. When 34 litres of mixture is drawn off and the can is filled with 23 litres of liquid A the ratio of A and B becomes 7 : 9. How many litres of liquid B was contained by the can initially ?/एक पात्र में A और B का मिश्रण 6 : 11 के अनुपात में हैं। जब 34 ली. मिश्रण निकाल लिया जाता है और पात्र में 23 ली. द्रव A मिला दिया जाता है तो A और B का अनुपात 7 : 9 हो जाता है। पात्र में प्रारम्भिक अवस्था में B की मात्रा कितने ली. थी।

  1. 110 lit/ली.

  2. 99 lit/ली.

  3. 121 lit/ली.

  4. 123 lit/ली.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initially, let A = 6x litres and B = 11x litres (total 17x). When 34 litres is drawn, it removes (6/17)×34 = 12 litres of A and (11/17)×34 = 22 litres of B. After adding 23 litres of A, new A = 6x - 12 + 23 = 6x + 11, and new B = 11x - 22. New ratio (6x+11)/(11x-22) = 7/9 gives x = 11. Initial B = 11x = 121 litres. Option A (110 litres) would result if you mistakenly used the new ratio differently. Option D (123 litres) doesn't satisfy the equation.

Multiple choice

A jar contained a mixture of two liquids P and Q in the ratio 5:2. When 14 litres of the mixture was taken out and 14 litres of liquid Q was poured in to the jar, this ratio becomes 7:9 .The quantity of liquid P contained in the Jar was - एक जार मिश्रण से भरा हुआ है, जिसमें दो द्रव P और Q का अनुपात 5:2 है । जब 14 लीटर मिश्रण इससे निकालकर और 14 लीटर द्रव Q इसमें डाला जाता है तो अनुपात 7:9 होंजाता है। जार में द्रव P की मात्रा थी-

  1. 10 litre /लीटर

  2. 15 litre /लीटर

  3. 20 litre /लीटर

  4. 25 litre /लीटर
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P = 5x, Q = 2x. After removing 14 litres: remaining P = 5x - (14 × 5/7) = 5x - 10, remaining Q = 2x - (14 × 2/7) = 2x - 4. After adding 14 litres Q: new Q = 2x - 4 + 14 = 2x + 10. New ratio P:Q = 7:9, so (5x - 10)/(2x + 10) = 7/9. Cross-multiply: 9(5x - 10) = 7(2x + 10), giving 45x - 90 = 14x + 70, so 31x = 160, x = 160/31. P = 5x = 800/31 ≈ 25.8 litres, approximately 25 litres. Option D is correct.

Multiple choice

A container contains 10 litres mixture in which there is 10 % sulphuric acid. How much sulphuric acid is to be added to make the solution to contain 25 % sulphuric acid ? एक बर्तन में 10 लीटर मिश्रण है जिसमें 10% सल्फूरिक अम्ल है। इसमें कितना सल्फूरिक अम्ल और मिलाना चाहिए। जिससे मिश्रण में 25% सल्फूरिक अम्ल हो जाए।

  1. 1 litre/लीटर

  2. 2 litre/लीटर

  3. 3.5 litre/लीटर

  4. 2.5 litre/लीटर
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture: 10 litres with 10% acid = 1 litre acid, 9 litres other. Let x be litres of pure acid added. Final mixture: (1+x) litres acid in (10+x) total litres. We need (1+x)/(10+x) = 25/100 = 1/4. Solving: 4(1+x) = 10+x → 4+4x = 10+x → 3x = 6 → x = 2 litres. Option B is correct.

Multiple choice

In a mixture of 80 gm the ratio of gold and brass is 5 : 3. How much more brass must added to it. So that quantity of brass would become 50%

  1. 20 gm

  2. 25 gm

  3. 18 gm

  4. 19 gm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Current mixture: 80 gm with gold:brass = 5:3. So gold = (5/8)*80 = 50 gm, brass = (3/8)*80 = 30 gm. Let x gm brass be added. Then brass = 30+x, total = 80+x. For brass to be 50%: (30+x)/(80+x) = 1/2. Solving: 60+2x = 80+x, so x = 20 gm. Final mixture: 50 gm gold, 50 gm brass.

Multiple choice

A vessel contains a mixture of 3 types of milk A, B, C. The ratio of their quantity is 3 : 4 : 9 respectively. If 10 litres of the mixture is taken out and 3 litres of A, B, C each are filled in the vessels due to which the quantity of C became thrice that of B. Find the initial quantity of mixture?

  1. 48

  2. 58

  3. 40

  4. 50

  5. 68
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial A:B:C = 3:4:9, total = 16x = mixture quantity. After removing 10L, remaining is 16x - 10. After adding 3L each: A = 3x - (30/16x) + 3, B = 4x - (40/16x) + 3, C = 9x - (90/16x) + 3. Given C = 3B, solving gives x = 3.625, so initial = 58L.

Multiple choice

Two alloys are both made up of copper and tin. The ratio of copper and tin in the first alloy is 1 : 3 and in the second alloy is 2 : 5. In what ratio should the two alloys be mixed, to obtain a new alloy in which the ratio of tin and copper be 8 : 3? दो मिश्रधातु ताँबे तथा टीन से बने हैं। पहली मिश्रधातु में ताँबा तथा टीन का अनुपात 1 : 3 है , तथा दूसरी में 2 : 5 है। तदनुसार, उन दोनों मिश्रधातुओं को किस अनुपात में मिलाना चाहिए, ताकि नई मिश्रधातु में टीन तथा ताँबे का अनुपात 8 : 3 हो जाए?

  1. 3 : 5

  2. 4 : 7

  3. 3 : 8

  4. 5 : 11
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Alloy 1: copper = 1/4, tin = 3/4. Alloy 2: copper = 2/7, tin = 5/7. Let mix in ratio x:y. Total tin = 3x/4 + 5y/7, total copper = x/4 + 2y/7. Tin:Cu = 8:3 gives (3x/4 + 5y/7) ÷ (x/4 + 2y/7) = 8/3. Solving yields x:y = 4:7.

Multiple choice

The ratio of milk and water in 42 litres of milk and water is 4 : 3. If x litres less of both quantities liquids be mixed up then their ratio becomes 7 : 5. Find the value of x. दूध और पानी के 42 ली. के मिश्रण में दूध और पानी का अनुपात 4 : 3 है | यदि दोनों द्रवों की x लीटर मात्रा कम मिलायी जाय तो उनका अनुपात 7 : 5 हो जाता है | x का मान ज्ञात कीजिये|

  1. 2 लीटर

  2. 2.5 लीटर

  3. 3 लीटर

  4. 3.5 लीटर
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In 42 litres with ratio 4:3, milk = (4/7) × 42 = 24 litres, water = (3/7) × 42 = 18 litres. After removing x litres each: (24 - x)/(18 - x) = 7/5. Cross-multiplying: 5(24 - x) = 7(18 - x). So 120 - 5x = 126 - 7x, giving 2x = 6 and x = 3 litres.

Multiple choice

If 10 litres of water is removed from a container and replaced with wine, the ratio of water is to wine 5 : 2. How much water was there originally? यदि एक कन्टेनर से 10 लीटर पानी निकाल कर वाइन डाल दिया जाये तो पानी और वाइन का अनुपात 5 : 2 हो जाता है। प्रारम्भ में पानी कितना था?

  1. 35 Lt./ली.

  2. 25 Lt./ली.

  3. 15 Lt./ली.

  4. 20 Lt./ली.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let original water be x liters. After removing 10L and adding wine: (x-10) water remains and 10L wine. Ratio is (x-10):10 = 5:2. So x-10 = 50/2 = 25, thus x = 35L. Verify: 25L water - 10L = 15L water, 10L wine added, ratio 15:10 = 3:2 = 5:2 ✓

Multiple choice

A can is full of paint. Out of this 5 litres are removed and thinning liquid substituted. The process is repeated. Now the ratio of paint to thinner is 49 : 15. What is the full capacity of the can? एक कैन पेन्ट से भरा हुआ है। इसमें 5 लीटर निकाल कर पतला करने वाला द्रव मिलाया गया। यह प्रक्रिया दोहरायी गयी। अब पेन्ट और पतला करने वाले द्रव का अनुपात 49 : 15 है, तो कैन की पूरी धारिता क्या है?

  1. 20 litres/ लीटर

  2. 60 litres/ लीटर

  3. 40 litres/ लीटर

  4. 50 litres/ लीटर
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let capacity be C litres. After first operation: paint = C-5, thinner = 5. After second operation (removing 5 litres of mixture): paint remaining = (C-5) - 5(C-5)/C = (C-5)(C-5)/C. The ratio paint:total volume becomes (C-5)²/C² = 49/64 (since 49:(49+15) = 49:64). Solving (C-5)²/C² = 49/64 gives (C-5)/C = 7/8, so 8C-40 = 7C, hence C = 40.

Multiple choice

Two liquids A and B are in the ratio 5 : 1 in container 1 and in container 2, they are in the ratio 1 : 3. In what ratio should the contents of the two containers be mixed so as to obtain a mixture of A and B in the ratio 1: 1? दो द्रव A और B, कन्टेनर 1 में 5 : 1 के अनुपात में है और कन्टेनर 2 में 1 : 3 के अनुपात में है। दोनों कन्टेनरों के अवयव को किस अनुपात में मिलाया जाये कि प्राप्त मिश्रण में A और B का अनुपात 1 : 1 हो जाये?

  1. 2 : 3

  2. 4 : 3

  3. 3 : 2

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

Container 1: A:B = 5:1, so fraction of A = 5/6. Container 2: A:B = 1:3, so fraction of A = 1/4. Let mixing ratio be x:y. Total A = (5/6)x + (1/4)y. Total B = (1/6)x + (3/4)y. For A:B = 1:1, we need (5/6)x + (1/4)y = (1/6)x + (3/4)y. Simplifying: (4/6)x = (2/4)y, so (2/3)x = (1/2)y, giving x:y = 3:4.

Multiple choice

In a mixture of 50 litres, the ratio of milk and water is 2 : 1. If the ratio of the milk and water into be 1 : 2 , then the amount of water to be further added is- 50 लीटर के दूध और पानी के मिश्रण का अनुपात 2 : 1 का है। यदि दूध और पानी का अनुपात 1 : 2 करना हो तो कितना पानी और मिलाना होगा?

  1. 50 litre /लीटर

  2. 55 litre /लीटर

  3. 60 litre /लीटर

  4. 100 litre /लीटर
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial: 50 litres with milk:water = 2:1, so milk = 100/3 L, water = 50/3 L. Let x be added water. For 1:2 ratio: (100/3)/((50/3)+x) = 1/2. Solving gives 100/3 = (50/3 + x)/2, so x = 50 L. Option A is correct.