### Aptitude questions and answers on Alligation and Mixture

1) A 60-liter mixture of milk and water contains 10% water. How much water must be added to make water 20% in the mixture?

1. 8 liters

2. 7.5 liters

3. 7 liters

4. 6.5 liters

The mixture has 10% water, so the milk would be 90% of 60 liters.

Milk = * 60 = 54 liters
100

∴Water = 60 - 54 = 6 liters

Let water to be added = x liters

Now,   6+x  * 100 = 20
60+x

6+x  =    1
60+x      5

30 + 5x = 60+x

30 - 60 = x - 5x

- 30 = - 4x

x =30  =7.5 liters
4

2) An alloy contains14 parts of tin and 100 parts of copper. What is the percentage of tin in the alloy?

1. 12.3%

2. 13%

3. 11.5%

4. 11%

In 114 parts of alloy, tin = 14 parts

∴Percentage of tin =  14  ∗100=12.3%
114

3) A 20-liter mixture contains 30% alcohol and 70% water. If 5 liters of water is added to the mixture, what will be the percentage of alcohol in the new mixture?

1. 22%

2. 23%

3. 24%

4. 25%

Initially, the mixture contains 30% alcohol =  30 ∗20=6 liters of alchol
100

And, 70% of water =  70 ∗20=14 liters of water
100

After adding 5 liters of water, the mixture contains (14+5) 19 liters of water and 6 liters of alcohol.

∴Percentage of alcohol = 6 ∗100=24%
25

4) In what ratio water must be mixed with milk costing Rs. 48 per liter to get a mixture worth Rs. 32 per liter ?

1. 2:3

2. 3:2

3. 3:4

4. 1:2

Apply allegation rule: ∴ Water = 16 = 1
Milk     32    2

Required ratio; water:milk = 1:2

5) A shopkeeper mixes 60 kg of sugar worth Rs. 30 per kg with 90 kg of sugar worth Rs. 40 per kg. At what rate he must sell the mixture to gain 20%?

1. Rs. 30 per kg

2. Rs. 34 per kg

3. Rs. 43.2 per kg

4. Rs. 38 per kg

Total cost price of (60+90)150 kg of mixture = (60*30+90*40)

= 1800+3600

= Rs. 5400

Cost Price per kg of mixture = 5400 = Rs. 36 per kg
150

Now, Required gain = 20%

∴Required selling price per kg of mixture = 120 ∗36 = Rs. 43.2 per kg
100

6) 700 ml of a mixture contains water and milk in the ratio of 2:8. How much water must be added to the mixture so that the ratio of water and milk becomes 3:8?

1. 75 ml

2. 65 ml

3. 70 ml

4. 60 ml

Milk in the 700 ml of mixture = 700 ∗ 8 =560ml
10

So, water in the mixture would be = 700 - 560 = 140 ml

Let water to be added = x ml

Now, 140+x = 3
560     8

1120+8x = 1680

8x = 1680 - 1120

8x= 560

X= 560 = 70 ml
8

7) A rice dealer bought 60 kg of rice worth Rs. 30 per kg and 40 kg of rice worth Rs. 35 per kg. He mixes the two and sells the mixture at Rs. 40 per kg. What is the percentage profit in this deal?

1. 18%

2. 21%

3. 23%

4. 25%

Total cost price of (60 + 40) 100kg of mixture = (60*30 + 40*35)

= 1800 + 1400

= Rs. 3200

Now, selling price of the mixture = 100 * 40 = Rs. 4000

Profit = 4000 - 3200 = Rs. 800

∴Required percentage profit = 800 ∗ 100 = 25%
3200

8) 1/2 and 1/4 parts of two bottles are filled with milk. The bottles are then filled completely with water and the content of bottles is poured into a container. Find the ratio of the milk and water in the container?

1. 3/5
2. 4/5
3. 2/3
4. 5/3

Let the capacity of each bottle = 1

Total capacity of two bottles = 1+1= 2

Quantity of milk in the first bottle = Quantity of milk in the second bottle = ∴The total quantity of milk in the two bottles = Hence the amount of water in the two bottles = ∴The required ratio of milk and water = 9) A bottle of whisky contains 40% alcohol. If we replace a part of this whisky by another whisky containing 20% alcohol, the percentage of alcohol becomes 28%. What quantity of whisky is replaced?

1. 3/5

2. 3/4

3. 4/5

4. 2/5 ∴The ratio of first and second whisky in the mixture

= 8:12 = 2:3

Now, the quantity of whisky replaced is equal to the quantity of the second whisky added.

∴The quantity of whisky replaced = 3
5

10) An alloy has copper and zinc in the ratio of 6:3 and another alloy has copper and tin in the ratio of 8:6. The equal weights of both the alloys are melted to form a new alloy. What will be the weight of tin per kg of the new alloy?

1. 4/14kg

2. 3/14kg

3. 3/12kg

4. 2/10kg

Weight of tin in the second alloy = Now, 2 kg of new alloy contains kg of tin.
∴Tin per kg of new allow would be = kg