A mixture contains wine and water in the ratio $5 : 1$. On adding $5$ litre of water, the ratio of wine to water becomes $5 : 2$. What is the quantity of wine in the mixture?

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Accepted Answer

**Solution:**

1. Let the quantity of wine be $5x$ litres and water be $x$ litres initially.

2. After adding $5$ litres of water, the quantity of water becomes $x + 5$ litres.

3. The new ratio of wine to water is given as $5 : 2$, so:
   $$\frac{5x}{x + 5} = \frac{5}{2}$$

4. Cross-multiply:
   $$2 	imes 5x = 5 	imes (x + 5)$$
   $$10x = 5x + 25$$

5. Simplify:
   $$10x - 5x = 25$$
   $$5x = 25$$
   $$x = 5$$

6. Quantity of wine:
   $$5x = 5 	imes 5 = 25 	ext{ litres}$$

**Answer:** None of these (since 25 ℓ is not listed among the options)

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