A mixture contains milk and water in a ratio of 9 ∶ 5. When 6 litres of water is added to this mixture, the ratio of milk and water becomes 9 ∶ 7, Find the quantity of milk in the mixture

Let's denote the quantity of milk in the mixture as $M$ liters and the quantity of water as $W$ liters.

Given the initial ratio of milk to water is 9:5, we can write: $\frac{M}{W} = \frac{9}{5}$ $M = \frac{9}{5}W \quad \text{(1)}$

When 6 liters of water is added, the new quantity of water becomes $W + 6$ liters. The new ratio of milk to water is given as 9:7, so we can write: $\frac{M}{W + 6} = \frac{9}{7}$ $M = \frac{9}{7}(W + 6) \quad \text{(2)}$

Now, we have two equations: $M = \frac{9}{5}W \quad \text{(1)}$ $M = \frac{9}{7}(W + 6) \quad \text{(2)}$

Since both expressions represent $M$, we can set them equal to each other: $\frac{9}{5}W = \frac{9}{7}(W + 6)$

To eliminate the fractions, we can multiply both sides by 35 (the least common multiple of 5 and 7): $35 \cdot \frac{9}{5}W = 35 \cdot \frac{9}{7}(W + 6)$ $7 \cdot 9W = 5 \cdot 9(W + 6)$ $63W = 45(W + 6)$

Now, distribute and solve for $W$: $63W = 45W + 270$ $63W - 45W = 270$ $18W = 270$ $W = \frac{270}{18}$ $W = 15$

Now that we have $W$, we can find $M$ using equation (1): $M = \frac{9}{5}W$ $M = \frac{9}{5} \cdot 15$ $M = 27$

Therefore, the quantity of milk in the mixture is 27 liters.