The ratio of milk and water in a mixture is 3 : 7. If we add 10 litres of water to the mixture, then the ratio becomes 1 : 3. Find the initial quantity of milk.

Given:

The ratio of milk and water in a mixture is 3:7.

If we add 10 litres of water to the mixture, then the ratio becomes 1:3.

Formula used:

Let the initial quantity of milk be 3x litres and the initial quantity of water be 7x litres.

After adding 10 litres of water, the quantity of water becomes (7x + 10) litres.

The new ratio is given as 1:3, so:

Calculation:

⇒ \(\dfrac{3x}{7x + 10} = \dfrac{1}{3}\)

Cross multiply to solve:

⇒ 3 × 3x = 1 × (7x + 10)

⇒ 9x = 7x + 10

⇒ 9x - 7x = 10

⇒ 2x = 10

⇒ x = 5

Initial quantity of milk = 3x = 3 × 5 = 15 litres

∴ The correct answer is option 1.