# Alligation and Mixture Questions -03

(01) A mixture of 30 liters contain milk and water in the ratio of 7: 3. How much water should be added to it so that the ratio of milk and water becomes 3: 7 ?

Given:
Mixture of milk and water = 30 litres

In the ratio = 7: 3

Amount of milk = 7/ (7 + 3) x 30

= (7/ 10) x 30

= 21 litres

Amount of water = 3/ (7 + 3) x 30

= (3/ 10) x 30

= 9 litres

I.e., in 30 litres of mixtures 21 litres of milk and 9 litres of water is added.

Now, it is to be noted that only water is added here so amount of milk will remain same throughout the mixture, so Let the total amount of water in the solution be x

Therefore, 21: x = 3: 7

21/ x = 3/7

x = 21 x 7/ 3

= 49 litres

Therefore, amount of water to be added = total amount of water in new solution – water present in old solution

= 49 – 9 = 40 litres

Ans.  Hence 40 litres of water is added.

(02) In 50 gm alloy of gold and silver, the gold is 80 % by weight. How much gold is mixed to this alloy so that the weight of gold would become 95%?

Given: Percentage of gold in 50 gm of alloy = 80 %

By allegations law,

n1  : n2 = 5 : 15 or 1: 3

Hence, the quantity of gold in the ratio = 3 x 50 gm = 150 gm

Ans. 150 gm of gold is to be mixed.

(03) There are 81 litres pure milk in a container. One – third of milk in the container is replaced by water. Again one – third of mixture is extracted and equal amount of water is added. What is the ratio of milk to water in the new mixture?

Given: initial quantity of milk = 81 litres = c

One- third of water is taken = (1/ 3 ) x 81 = 27 litres  = x

No. Of process = 2 = n

Quantity of water = 81 – 36 = 45 litres

Therefore, ratio of milk to water in the new mixture = 36: 45

= 4: 5

Ans. The ratio of milk to water in the mixture is 4: 5

(04) In 80 litres mixture of milk and water the ratio of amount of  milk to that of water is 7: 3.In order to make this ratio 2:1 how many litres of water should be added?

Given: Mixture of milk and water = 80 litres

Ratio of milk to water = 7: 3

Amount of milk = [7/ (7 + 3)] x 80 = 56 litres

Amount of water [3/ (7 + 3)] x 80 = 24 litres

In order to be change the ratio water is added here I.e., amount of milk will be constant here, Let the amount of water in new mixture be x

Therefore, 56: x = 2: 1

56/ x = 2/1

x = 56/ 2 = 28 litres

Amount of water added = amount of water in (new mixture – old mixture)

= 28 – 24

= 4 litres

Ans. Therefore, 4 litres of water is added

(05) The milk and water in a mixture are in the ratio 7: 5. When 15 litres of water are added t it, the ratio of milk and water in the new mixture becomes 7: 8. The total quantity of water in the new mixture is:

Given: milk: water = 7: 5 in old mixture

After adding 15 litres of water

Milk: water = 7: 8 in new mixture

Here amount of milk is constant from beginning,

Rise in water = 8 – 5 = 3 units

3 units = 15 litres (according to question)

1 unit = 15/ 3 = 5 litres

Therefore, amount of water in new mixture = 8 x 5 = 40 litres

Ans. Total amount of  water is 40 litres.