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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