Question

A mixture contains milk and water in the ratio of 5 ∶ 3. If 10 litres of milk is added to the mixture, the ratio becomes 7 ∶ 3. How many litres of milk is in the mixture initially?

1. 20 litres
2. 25 litres
3. 15 litres
4. 45 litres

Answer 1

Correct Answer - Option 2 : 25 litres

Given:

The ratio of milk to water in the mixture is 5 ∶ 3

Concept used:

(Amount of milk + 10)/Amount of water = 7 ∶ 3

Calculation:

Let the amount of milk = 5Y litres

And the amount of water = 3Y litres

If 10 liters of milk is added to milk then amount of milk = (5Y + 10) liters

Since ratio becomes 7∶3 after adding milk

Therefore, (5Y + 10)/3Y = 7/3

⇒ (7 × 3Y) = {3 × (5Y + 10)}

⇒ 21Y = 15Y + 30

⇒ 21Y – 15Y = 30

⇒ 6Y = 30

⇒ Y = 30/6 = 5

Amount of milk = 5Y = 5 × 5 = 25

∴ Initial quantity of milk was 25 litres