Question : A mixture of 70 litres of wine and water contains 10% of water. How much water must be added to make the water $12 \frac{1}{2}\%$ of the resulting mixture?
Option 1: 5 litres
Option 2: 3 litres
Option 3: 2 litres
Option 4: 4 litres
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Correct Answer: 2 litres
Solution : Initial quantity of mixture = 70 litres Quantity of water in the initial mixture = 10% of 70 = 7 litres Let $x$ litres water be added. The final quantity of mixture = 70 + $x$ Quantity of water in the final mixture = $12\frac{1}{2}$% of (70 + $x$) According to the question, $7 + x = \frac{25}{200} × (70 + x)$ ⇒ $8(7 + x) = 70 + x$ ⇒ $56 + 8x = 70 + x$ ⇒ $7x = 14$ $\therefore x = 2$ litres Hence, the correct answer is 2 litres.
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