Question

Milkman has a container filled with a mixture of milk and water which are in the ratio of 7 : 3. How many parts of the mixture needs to be removed and replaced from the water to obtain milk and water in ratio of 1 : 1?
1. 2/3
2. 2/7
3. 2/5
4. 1/7
5. None of the above

Answer 1

Correct Answer - Option 2 : 2/7

Given:

Initial ratio of milk to water ratio = 7 : 3

Calculations:

Here, let milk in mixture be 7 liters and water be 3 liters

⇒ milk : water = 7 : 3

⇒ Let, X to be quantity of mixture withdrawn and replaced with water.

⇒ (7 - 7X/10)/(3 - 3X/10 + X) = 1/1

⇒ 7 - 7X/10 = 3 - 3X/10 + X

⇒ 7 - 3 = 7X/10 - 3X/10 + X

⇒ 4 = 14X/10

⇒ X = 20/7

⇒ Total quantity = 10 liters

⇒ Quantity withdrawn = 20/7 × 1/10

⇒ Quantity withdrawn = 2/7

∴ 2/7^th of mixture needs to be replaced with water.