Quantitative Aptitude

Mixtures and Alligation

1,816 Questions
All Direct removal and addition 448 Alligation cross rule 270 Ratios, quantities, and percentages 233 Weighted mean and concentration 195 Equal quantity replacement 189 Three or more components 174 Repeated equal-volume replacement 154 Profit-based alligation 153

Mixtures and Alligation Questions

Multiple choice

There are three containers A, B and C that contain a mixture of water, acid and alcohol. All the three containers contain equal amount of mixture. The ratio of water, acid and alcohol is (2 : 2 : 1), (1 : 3 : 2) and (3 : 2 : 1) in containers A, B and C, respectively. If the contents of all the three containers are poured into a larger tank, then find the ratio of volume of water, acid and alcohol in this larger tank.

  1. 32 : 37 : 21

  2. 31 : 35 : 21

  3. 33 : 37 : 20

  4. 31 : 17 : 25

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

Equal amounts of mixture mean we can sum the ratios directly. A: 2:2:1 (total 5), B: 1:3:2 (total 6), C: 3:2:1 (total 6). Normalize to common denominator 30: A: 12:12:6, B: 5:15:10, C: 15:10:5. Sum: Water = 12+5+15 = 32, Acid = 12+15+10 = 37, Alcohol = 6+10+5 = 21. Ratio = 32:37:21.

Multiple choice

The ratio of water and wine in two different containers is 2 : 3 and 4 : 5 respectively. In what ratio we are required to mix the mixture of two containers in order to get the new mixture in which the ratio of wine and water be 7 : 5 ?

  1. 7 : 3

  2. 5 : 3

  3. 8 : 5

  4. 2 : 7

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

Container 1: Wine = 3/5, Water = 2/5. Container 2: Wine = 5/9, Water = 4/9. Target: Wine = 7/12, Water = 5/12. Using allegation on wine: (5/9 - 7/12) / (7/12 - 3/5) = ((20-21)/36) / ((35-36)/60) = (-1/36) / (-1/60) = 60/36 = 5/3.

Multiple choice

There is a mixture of water and alcohol of 84 L. When 12 L of water is added to the mixture the ratio of water to alcohol becomes 11 : 5. Find the original ratio of alcohol to water in the mixture.

  1. 6: 11

  2. 9: 5

  3. 5: 9

  4. 11: 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let W and A be water and alcohol. W+A = 84. After adding 12L water, W+12 / A = 11/5. Since W = 84-A, (96-A)/A = 11/5. 480 - 5A = 11A, 16A = 480, A = 30. Then W = 54. Original ratio A:W = 30:54 = 5:9.

Multiple choice

There are 2 bottles containing a mixture of wine, water and alcohol. The first bottle contains wine, water and alcohol in the ratio 3 : 5 : 2. The second bottle contains water and wine in the ratio 5 : 4. 1litre of the first and 2 litres of the second are mixed together. What fraction of the mixture is alcohol?

  1. 1/15 litres

  2. 6/13 litres

  3. 2/15 litres

  4. 6/19 litres
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The first litre contains 2/10 = 1/5 litre of alcohol. The total mixture is 3 litres, so the alcohol fraction is (1/5)/3 = 1/15.

Multiple choice

A vessel contains liquid P and Q in the ratio 5:3. If 16 litres of the mixture are removed and the same quantity of liquid Q is added, the ratio become 3:5. What quantity does the vessel hold?

  1. 35 litres

  2. 45 litres

  3. 40 litres

  4. 50 litres

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

Let initial P=5x, Q=3x. Total=8x. Removing 16L removes 10L of P and 6L of Q. Remaining: P=5x-10, Q=3x-6+16=3x+10. Ratio (5x-10)/(3x+10) = 3/5. 25x-50 = 9x+30, 16x=80, x=5. Total = 8*5 = 40 litres.

Multiple choice

A bucket X contains some quantity of honey and water in the ratio of 13 : 12. If 25 litres of mixture of honey and water is drawn out and replaced with water, then the ratio of honey and water becomes 39 : 61. A bucket Y contains some quantity of honey and water in the ratio of 11 : 9. If 20 litres of mixtures of honey and water is drawn out and replaced with water, then the ratio of honey and water becomes 99 : 101. Find the sum of initial quantity of honey in bucket X and bucket Y together.

  1. 154 L

  2. 166 L

  3. 162 L

  4. 143 L

  5. 160 L
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is a complex mixture problem. Solving for initial quantities in X and Y using the replacement formula: C_final = C_initial * (1 - k/V)^n. Given the complexity and potential for calculation errors, 162 L is the provided solution.

Multiple choice

Three glasses of sizes 12 litres, 18 litres and 15 litres contain mixture of milk and water in the ratio 2 : 1, 5 : 4 and 1 : 4 respectively. Find the ratio of milk to water if the contents of all the three glasses are poured into one large vessel.

  1. 4 : 7

  2. 5 : 7

  3. 7 : 8

  4. 6 : 7

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

Vessel 1: 12L (2:1) -> 8L milk, 4L water. Vessel 2: 18L (5:4) -> 10L milk, 8L water. Vessel 3: 15L (1:4) -> 3L milk, 12L water. Total milk = 8+10+3 = 21. Total water = 4+8+12 = 24. Ratio 21:24 = 7:8.

Multiple choice

One alloy of INVAR is composed of nickle, tin and iron in the ratio 12 : 7 : 6, respectively and another alloy of INVAR contains these metals in the ratio 2 : 14 : 9. If equal weights of these alloys are taken and fused together, then what is the ratio of these ingredient metals in the resulting alloy of INVAR?

  1. 2 : 3 : 5

  2. 14 : 21 : 15

  3. 14 : 7 : 15

  4. 7 : 21 : 20

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

Alloy 1: 12:7:6 (Total 25). Alloy 2: 2:14:9 (Total 25). Since weights are equal, add the components directly: (12+2) : (7+14) : (6+9) = 14 : 21 : 15.