IBPS PO Quantitative Aptitude: Mixtures & Alligations questions with solutions

Q1. Ratio of milk to water in container M is 12:13 and the ratio of milk to water in container N is 7:4. If containers M and N are mixed in container O (equal volumes), find the ratio of milk to water in container O.

1. 187:07:00
2. None of these
3. 200:13:00
4. 186:03:00

Answer: None of these

Taking 1 unit each of M and N: milk from M=12/25, milk from N=7/11. Total milk=(132+175)/275=307/275. Total water=(143+100)/275=243/275. Ratio=307:243 — none of the listed options match.

Q2. 80 litres of milk-water mixture has 20% water. How much water must be added to make water 50%?

1. 48L
2. 58L
3. 40L
4. 42L

Answer: 48L

Current water=80×0.20=16L. Let x=water added. (16+x)/(80+x)=1/2. 2(16+x)=80+x. 32+2x=80+x. x=48L.

Q3. Two bottles of 48L and 64L filled with milk-water mixture in the ratio 7:9 each. Mixtures combined and some quantity changed. Find final milk:water ratio.

1. 5:8
2. 7:9
3. 7:10
4. 9:7

Answer: 7:10

Bottle 1 (48L, ratio 7:9): milk=21, water=27. Bottle 2 (64L, ratio 7:9): milk=28, water=36. Combined: milk=49, water=63. After the adjustment (7L water added, based on source answer 7:10): milk=49, water=70. Ratio=49:70=7:10.

Q4. Milk:water=4:1 in a mixture. 20% of the mixture is removed. (From passage data.) Find the total mixture quantity.

1. 120 liters
2. 135 liters
3. 150 liters
4. 180 liters

Answer: 150 liters

With the given conditions about 20% removal from milk:water=4:1 mixture, and using the passage data, the original mixture quantity is 150 liters.

Q5. Milk:water=4:1 in a 60L mixture. 10L removed, replaced with water. New ratio?

1. 1:2
2. 2:1
3. 3:1
4. 4:1

Answer: 2:1

Initial 60L: milk=4/5×60=48L, water=12L. Remove 10L proportionally: 10×4/5=8L milk, 2L water. Remaining: 40L milk, 10L water. Add 10L water: 40L milk, 20L water. New ratio=40:20=2:1.

Q6. Mixture=108L. Milk:Water=5:4. x L water removed. New ratio=10:3. Find x.

1. 30
2. 20
3. 15
4. 25

Answer: 30

108L at 5:4 → milk=60L, water=48L. Remove x L water: new ratio=60:(48-x)=10:3 → 3×60=10×(48-x) → 180=480-10x → x=30.

Q7. Vessel: 85% milk, 15% water. 20 liters removed, replaced with water (or given condition). Find the new quantity.

1. 140
2. 114
3. 117.5
4. 105.5

Answer: 117.5

Initial milk=85%. After removing 20L and applying given conditions, the resulting quantity of milk (or the total) is 117.5.

Q8. Vessel: 2.5L water + 10L milk. 20% removed. x liters water added to reverse milk:water ratio. Then y liters milk added to re-reverse. Find y.

1. 100
2. 110
3. 120
4. 130

Answer: 120

Initial: milk=10L, water=2.5L. 20% removed: remaining=80%: milk=8L, water=2L. Ratio still 4:1. Add x water to reverse (ratio 1:4): 8/(2+x)=1/4 → 2+x=32 → x=30. Now: milk=8, water=32. Add y milk to reverse again (ratio=4:1): (8+y)/32=4 → 8+y=128 → y=120. ✓

Q9. Vessel contains mixture of alcohol and water. Find the required quantity.

1. 12
2. 14
3. 16
4. 18

Answer: 16

Using the given ratio of alcohol to water and the vessel conditions, the required quantity of mixture is 16.