In a milk shoppe there are three varieties of milk, ‘pure’, ’Cure’ and ‘Lure'.

Ques - In a milk shoppe there are three varieties of milk, ‘pure’, ’Cure’ and ‘Lure’ . The ‘Pure’ milk has 100% concentration of milk. The ratio of milk is to water in the ‘Cure’ is 2:5 and in the Lure it is 3:8 respectively. Sonali purchased 14 liters of Cure and 22 litres of Lure milk and mixed them. If she wanted to make the concentration of milk in the mixture of purchased milk to 50% .How many litres of ‘pure’ milk she is needed?

(a) 6 litres

(b) 8 litres

(c) 16 litres

(d) 18 litres

Solution - 

Given,

There are three varieties of milk = pure, cure, lure

The Pure milk has 100% concentration of milk.

The ratio of milk is to water in the Cure = 2 : 5

And,

Sonali purchased cure = 14 litres

So,

Quantity of Milk in cure = 4 litres

Quantity of Water in cure = 10 litres

Similarly,

The ratio of milk is to water in the Lure = 3 : 8

And,

Sonali purchased Lure = 22 litres

So,

Quantity of Milk in Lure = 6 litres

Quantity of Water in Lure = 16 litres

When it is being mixed it has,

 Quantity of milk = 4 + 6 litres

= 10 litres

Quantity of water = 10 + 16 litres

= 26 litres

If she wanted to make the concentration of milk in the mixture of purchased milk to 50%.

Milk             Water

10                26

We have to make both the milk and water is 50% in the mixture and we have 26 litres of water and 10 litres of milk in the mixture. so, we have to add 16 litres of milk in the mixure to make it 26 litres.

Now,

Milk            Water

10 + (16)     26

26                26

Therefore,

She is needed 16 litres of ‘pure’ milk .

Hence,

The correct answer is option (c) 16 litres.

Thank you