Two containers have mixtures of milk and water, respectively, in the ratios 3 ∶ 2 and 6 ∶ 5. In what ratio should the contents be mixed so that the ratio of milk to water in the final mixture is 4 ∶ 3?

Two containers have mixtures of milk and water, respectively, in the ratios 3 ∶ 2 and 6 ∶ 5.
The ratio of milk to water in the final mixture is 4 : 3.

Let P unit of the first mixture is added to Q unit of the second mixture.
So, in P unit of first mixture,

Amount of milk present = 3/5 × P = 3P/5
Amount of water present = 2/5 × P = 2P/5

So, in Q unit of second mixture,
Amount of milk present = 6/11 × Q = 6Q/11
Amount of water present = 5/11 × Q = 5Q/11

According to the question,
(3P/5 + 6Q/11) ÷ (2P/5 + 5Q/11) = 4 ÷ 3
⇒ {(33P + 30Q)/55} ÷ {(22P + 25Q)/55} = 4 ÷ 3
⇒ 99P + 90Q = 88P + 100Q
⇒ 11P = 10Q
⇒ P : Q = 10 : 11

∴ In 10 : 11 the contents should be mixed so that the ratio of milk to water in the final mixture is 4 ∶ 3.