Question

A mixture contains milk and water in the ratio $$5 : 1$$. On adding 5 litres of water, the ratio of milk to water becomes $$5 : 2$$. Find the quantity of milk in the original mixture.

Answer 1

Let the quantity of milk and water in the original mixture be $$5x$$ litres and $$x$$ litres respectively. 

When 5 litres of water is added, the new quantity of water is $$(x + 5)$$ litres. 

New ratio: $$\frac{5x}{x + 5} = \frac{5}{2}$$ 

Cross-multiply: $$2(5x) = 5(x + 5)$$ 

$$10x = 5x + 25$$

$$5x = 25$$

$$\implies x = 5$$ 

Quantity of milk in original mixture = $$5x = 5 \times 5 = 25\text{ litres}$$.