The ratio of milk to water in 80 litres of a mixture is 7 : 3. The quantity of water (in litres) to be added to it to make the ratio 2 : 1 is :

1. 4

2. 5

3. 6

4. 8

Let the initial quantities of milk and water be 7x and 3x respectively.

Given,

The total volume of the mixture is 80 litres.

⇒ 7x + 3x = 80

⇒ 10x = 80

⇒ x = $\dfrac{80}{10}$

⇒ x = 8.

Initial Quantity of Milk : 7x = 7 × 8 = 56 litres

Initial Quantity of Water : 3x = 3 × 8 = 24 litres

Let W be the quantity of water added to the mixture.

The quantity of milk remains unchanged.

Water = 24 + W

The new ratio of milk to water is required to be 2 : 1.

⇒ $\dfrac{56}{24 + W} = \dfrac{2}{1}$

⇒ 56 = 2(24 + W)

⇒ 56 = 48 + 2W

⇒ 2W = 56 - 48

⇒ 2W = 8

⇒ W = $\dfrac{8}{2}$

⇒ W = 4.

The quantity of water to be added is 4 litres.

Hence, option 1 is the correct option.