Quantitative Aptitude

Mixtures and Alligation

1,816 Questions
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Mixtures and Alligation Questions

Multiple choice

A bucket contains a mixture of milk and water in the ratio of 8:5. When 78 liters of the mixture is taken out and 24 liters of water is added, the ratio of milk and water becomes 8:13. How much quantity of milk does the bucket have initially?

  1. 64 liters

  2. 120 liters

  3. 80 liters

  4. 84 liters

  5. 72 liters
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let milk=8x, water=5x (total=13x). After removing 78L (milk removed=48L, water removed=30L): milk=8x-48, water=5x-30. Adding 24L water: water=5x-30+24=5x-6. New ratio: (8x-48)/(5x-6)=8/13. Cross-multiply: 104x-624=40x-48. Solving gives 64x=576, so x=9. Initial milk=8x=72L. Option E is correct.

Multiple choice

4 litre of a solution having 10% acid was mixed with 5 litre of a solution having 16% acid. Six litre of pure acid was then added to the resulting solution. The concentration of acid in the final solution is: 10% अम्ल वाले 4 लीटर घोल को 16% अम्ल वाले 5 लीटर घोल में मिलाया गया है उसले बाद उस मिश्रण में 6 लीटर शुद्ध अम्ल भी मिलाया गया। अंतिम घोल में अम्ल की सांद्रता कितनी होगी?

  1. 48%

  2. 50%

  3. 54%

  4. 60%

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

First solution: 4L with 10% acid = 0.4L acid. Second: 5L with 16% acid = 0.8L acid. Mixed: 1.2L acid in 9L solution. Add 6L pure acid: total acid = 7.2L, total volume = 15L. Concentration = (7.2/15) × 100 = 48%.

Multiple choice

A drum contains 40 litres of milk. One-fourth of the milk is taken out and replaced with water. Then, half of the mixture is taken out and replaced with water. What is the respective quantity of milk and water left in the drum?

  1. 15 litres and 25 litres

  2. 10 litres and 30 litres

  3. 20 litres and 20 litres

  4. 25 litres and 15 litres
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial: 40 liters milk, 0 water. After removing 1/4 and adding water: milk = 40 - 10 = 30 liters, water = 10 liters. After removing half the mixture and adding water: half of 40 = 20 removed, which contains proportionally 15 milk and 5 water. Remaining: 15 milk, 5 water. Adding 20 water: milk = 15 liters, water = 5 + 20 = 25 liters. Final: 15 milk, 25 water.

Multiple choice

In a mixture of water and spirit water is 40%. When 25 liter water is added in the mixture percentage of water increased to 60%. Find the quantity of spirit in the mixture. पानी और स्पिरिट के मिश्रण में पानी 40% है जब मिश्रण में 25 लीटर पानी मिलाया जाता है तो मिश्रण में पानी का प्रतिशत बढ़कर 60% हो जाता है। मिश्रण में स्पिरिट की मात्रा ज्ञात कीजिये।

  1. 24 liter 24 लीटर

  2. 36 liter 36 लीटर

  3. 15 liter 15 लीटर

  4. 30 liter 30 लीटर

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

Let initial mixture = 100 liters. Water = 40 liters, Spirit = 60 liters. After adding 25 liters water: total = 125 liters, water = 65 liters. Given water becomes 60%: 65/125 = 52%, not 60%. Let initial mixture = x liters. Water = 0.4x, Spirit = 0.6x. After adding 25L water: water = 0.4x + 25, total = x + 25. Given (0.4x + 25)/(x + 25) = 0.60. Solving: 0.4x + 25 = 0.6x + 15, so 10 = 0.2x, x = 50. Spirit quantity = 0.6 × 50 = 30 liters, which is option D.

Multiple choice

In two alloys A and B the ratio of zinc to copper is 4:5 and 2:7 respectively. Eighteen kg of the alloy A and 45 kg of the alloy B are mixed together to form a new alloy. What will be the ratio of Zinc and copper in the new alloy? दो मिश्र धातुओं A और B में जिंक का तांबे से अनुपात क्रमश: 4: 5 और 2: 7 है। मिश्र धातु A के 18 किलोग्राम और 45 किलो मिश्र धातु B को एक नए मिश्र धातु के रूप में मिश्रित किया जाता है। नए मिश्र धातु में जिंक और तांबे का अनुपात क्या होगा?

  1. 4:5

  2. 2:5

  3. 3:7

  4. 2:3

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

Alloy A: Zinc:Copper = 4:5, total 9 parts. In 18kg: Zinc = (4/9)×18 = 8kg, Copper = (5/9)×18 = 10kg. Alloy B: Zinc:Copper = 2:7, total 9 parts. In 45kg: Zinc = (2/9)×45 = 10kg, Copper = (7/9)×45 = 35kg. New alloy: Total Zinc = 8 + 10 = 18kg, Total Copper = 10 + 35 = 45kg. Ratio = 18:45 = 2:5 after simplifying (dividing by 9). This matches option B.

Multiple choice

Two vessels contain mixtures of milk and water in the ratio of 4:9 in the first vessel and in the ratio of 2:7 in the second. In what ratio should the contents of these two vessels be mixed such that the resultants mixture has milk and water in the ratio of 2:5? दो पात्रों में दूध और पानी का मिश्रण जिसमें पहले पात्र में 4 : 9 के अनुपात में दूसरे में 2: 7 के अनुपात में हैं। किस अनुपात में इन दो पात्रों की मात्रा को मिश्रित किया जाना चाहिए ताकि परिणामी मिश्रण में दूध और पानी 2: 5 के अनुपात में हो?

  1. 26:9

  2. 14:10

  3. 25:18

  4. 22:8

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

Vessel 1 has milk:water = 4:9, so milk fraction = 4/13. Vessel 2 has milk:water = 2:7, so milk fraction = 2/9. Target mixture needs milk:water = 2:5, so milk fraction = 2/7. Using allegation: (2/7 - 2/9) : (4/13 - 2/7) = 4/63 : 2/91 = 26:9. Mix vessels in ratio 26:9. Option A is correct. Options B, C, D are incorrect ratio calculations.

Multiple choice

In a mixture of milk and water the proportion of water by weight was 60\%. If in 50 l of mixture 10 l water was added, what would be the percentage of water?
  1. $45 \frac{1}{2} \%$
  2. $72 \%$
  3. $66 \frac{2}{3} \%$
  4. $35 \%$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In the original 50 litre mixture, water is 60% by weight, so water = 0.60 × 50 = 30 litres and milk = 20 litres. After adding 10 litres of water, the total water becomes 40 litres and total mixture becomes 60 litres. The new water percentage is (40/60) × 100 = 66.67% or 66 2/3%.

Multiple choice

A vessel contains a mixture of two liquids A and B in the ratio 2 : 3. When 8 liters of the mixture is taken out and replaced with B, the ratio of A and B becomes 6 : 11. How much of the mixture was there initially?

  1. 30 liter

  2. 68 liter

  3. 45 liter

  4. 64 liter
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let initial mixture be x liters. Initial A = 2x/5, B = 3x/5. Removing 8L removes A = 16/5 L, B = 24/5 L. After adding 8L of B: new A = 2x/5 - 16/5, new B = 3x/5 - 24/5 + 8. New ratio (2x - 16)/(3x + 16) = 6/11. Solving: 22x - 176 = 18x + 96, so 4x = 272, x = 68L. Option A is incorrect. Option C would give ratio 6:13. Option D would give ratio 6:12.

Multiple choice

A jar was full of sugar solution. A person used to draw out 20% of the solution from the jar and replace with salt solution. He performs the same process 4 times and thus there was only 512 gm of sugar left in the jar, the rest part of the jar was filled with the salt solution. What was the initial amount of sugar in the jar?

  1. 0.25 kg

  2. 1.15 kg

  3. 1.00 kg

  4. 1.25 kg
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Each operation removes 20% of sugar, leaving 80%. After 4 operations, remaining sugar = initial × 0.8⁴ = initial × 0.4096. Given remaining sugar = 512 gm = 0.512 kg, so initial = 0.512/0.4096 = 1.25 kg. Option A would give 208.4 gm remaining. Option B would give 958.4 gm remaining. Option C would give 833.3 gm remaining.

Multiple choice

Mixture of water and alcohol is 40 litres, in which water is 60% of alcohol. Find the quantity of water added in the mixture so that water becomes 20% more than the alcohol.

  1. 24L

  2. 15L

  3. 12L

  4. 20L
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let alcohol = A, water = W. Given W = 0.6A and W + A = 40. Solving: 1.6A = 40, so A = 25 litres, W = 15 litres. After adding x litres of water, new water = 15 + x. Given water is 20% more than alcohol: 15 + x = 1.2 x 25 = 30, so x = 15 litres. The key is understanding percentages and setting up the correct equation.

Multiple choice

In what ratio should two qualities of Tea having the rates of Rs 40/kg and Rs 30/kg be mixed in order to get a mixture that would have rate of Rs 35 per kg ?

  1. 1:3

  2. 1:2

  3. 1:1

  4. 1:4

  5. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using allegation method: The target price of Rs 35/kg lies exactly midway between Rs 40/kg and Rs 30/kg. When the desired price is exactly in the middle, equal quantities of both varieties are needed. Therefore, the ratio is 1:1.

Multiple choice

In a mixture of milk and water, the proportion of milk by weight is 60%. If from the 80 gm mixture, 20 gm of mixture is taken out and 6 gm of pure water is added to the mixture then find the ratio of milk and water in the new mixture.
  1. $5 : 6$
  2. $6 : 5$
  3. $4 : 3$
  4. $3 : 2$
  5. $7 : 6$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial mixture: 80 gm with 60% milk = 48 gm milk, 32 gm water. Removing 20 gm removes proportionally: 48 × (20/80) = 12 gm milk, 32 × (20/80) = 8 gm water. Remaining: 36 gm milk, 24 gm water. Adding 6 gm water: 36 gm milk, 30 gm water. Ratio = 36:30 = 6:5. Option B is correct.

Multiple choice

In a mixture of milk and water, the proportion of milk by weight is 60%. If from the 80 gm mixture, 20 gm of mixture is taken out and 6 gm of pure water is added to the mixture then find the ratio of milk and water in the new mixture. दूध और पानी के मिश्रण में वजन के हिसाब से दूध का अनुपात 60% है। यदि 80 ग्राम मिश्रण में से 20 ग्राम मिश्रण निकाल लिया जाए और मिश्रण में 6 ग्राम शुद्ध पानी मिला दिया जाए तो नए मिश्रण में दूध और पानी का अनुपात ज्ञात कीजिए।

  1. 3 : 5

  2. 6 : 5

  3. 4 : 3

  4. 3 : 2

  5. 7 : 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In 80 gm mixture with 60% milk, milk = 48 gm, water = 32 gm. Removing 20 gm removes same proportion: 12 gm milk, 8 gm water. Remaining: 36 gm milk, 24 gm water. Adding 6 gm water gives 36 gm milk, 30 gm water. Ratio = 36 : 30 = 6 : 5.

Multiple choice

A mixture is made by mixing alcohol and water in the ratio (13 ∶ 7). If (3m) litres of alcohol and (5m) litres of water is mixed in 120 litres of mixture, the new ratio becomes (15 ∶ 17). Find the quantity of the new mixture.

  1. 289 litres

  2. 352 litres

  3. 316 litres

  4. 297 litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial 120L mixture has 78L alcohol and 42L water (13:7 ratio). After adding 3m alcohol + 5m water, new ratio (78+3m)/(42+5m) = 15/17. Cross-multiply: 17(78+3m) = 15(42+5m), giving 1326+51m = 630+75m, so 24m=696, m=29. Total new mixture = 120+3(29)+5(29) = 352L.

Multiple choice

8 litres of wine are drawn and replaced with water from a cask full of pure wine and the operation is repeated three more times. If the ratio of wine and water left in the cask are now 16:65, how much wine was originally held by the cask? 8 लीटर वाइन निकाली जाती है और शुद्ध शराब से भरे एक पीपे से पानी के साथ प्रतिस्थापित किया जाता है और प्रक्रिया को तीन बार दोहराया जाता है। यदि पीपे में बचे हुए शराब और पानी का अनुपात अब 16:65 है, तो मूल रूप से पीपे में कितनी शराब थी?

  1. 18 litres 18 लीटर

  2. 24 litres 24 लीटर

  3. 32 litres 32 लीटर

  4. 42 litres 42 लीटर

  5. 21 litres 21 लीटर
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let initial wine = x litres. After 4 operations of removing 8L and replacing with water, wine left = x(1 - 8/x)^4. Wine:water = 16:65 means wine is 16/81 of total. So x(1 - 8/x)^4 = 16x/81. Solving gives (1 - 8/x)^4 = 16/81, so 1 - 8/x = 2/3, giving x = 24. B is correct.