a) $$5\frac{2}{5}{\text{ litres}}$$
b) $$5\frac{2}{3}{\text{ litres}}$$
c) $$4\frac{1}{2}{\text{ litres}}$$
d) $$3\frac{3}{4}{\text{ litres}}$$
Answer: a
Explanation: The first mixture contains wine and water in the ratio of 3 : 2
Wine in 3 liters of mixture = $$\frac{3}{5} \times 3 = \frac{9}{5}$$
Water in 3 liters of mixture = $$\frac{2}{5} \times 3 = \frac{6}{5}$$
Let us consider that the first mixture is mixed with the second mixture that has quantity as 9x liters (4x liters of wine and 5x liters of water).
After mixing,
The total quantity of wine = Total quantity of water
$$\eqalign{
& \frac{9}{5} + 4x = \frac{6}{5} + 5x \cr
& x = \frac{9}{5} – \frac{6}{5} \cr
& x = \frac{3}{5} \cr} $$
Second Mixture required = 9x = $$9 \times \frac{3}{5}$$ = $$5\frac{2}{5}{\text{ litres}}$$
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