A mixture contains wine and water in the ratio 3:2 and another mixture contains them in the ratio 4: 5. How many liters of the second mixture must be mixed with 3 liters of first mixture so that the resultant mixture may contain equal quantities of wine and water?

\(5\frac{2}{5}\) liters

The former mixture contains wine and water in a ratio of 3:2

3 liters of the mixture contains 1.8 liters of wine and 1.2 liters of water to maintain a 3:2 ratio.

Let there be 4x liters of wine and 5x liters of water.

After mixing,

Quantity of  wine = Quantity of water

⇒ 1.8 + 4x = 1.2 + 5x

⇒ x = 0.6 liters

⇒ 9x = 9 × 0.6 = 5.4 liters

∴ The latter mixture mixed with the 3 liters of the former mixture is 5.4 liters.