Two vessels contain milk and water in the ratio 1:2 and 2:3. If both vessels are mixed in ratio 1: 1, find the ratio of milk and water in new mixture.

11 : 19

Let two vessels be A and B

The ratio of milk and water in A = 1 ∶ 2 → 3 unit

The ratio of milk and water in B = 2 ∶ 3 → 5 unit

Now, the LCM of 3 and 5 is 15 

The new ratio of milk and water in A = (1 ∶ 2) × 5 

The new ratio of milk and water in B = (2 ∶ 3) × 3 × 1

The ratio of the milk and water in new mixture = (1 × 5 + 2 × 3) ∶ (2 × 5 + 3 × 3)

⇒ 5 + 6 ∶ 10 + 9

⇒ 11 ∶ 19 

∴ The ratio of the milk and water in new mixture is 11 ∶ 19.