Question : 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.
Option 1: 30 litres
Option 2: 18 litres
Option 3: 27 litres
Option 4: 15 litres
Correct Answer: 27 litres
Solution :
Let the initial quantity of milk as $9x$ litres and the initial quantity of water as $5x$ litres.
When 6 litres of water is added, the quantity of milk remains the same $9x $ litres, but the quantity of water increases to $(5x + 6)$ litres.
The new ratio of milk to water is 9 : 7.
$⇒\frac{9x}{5x + 6} = \frac{9}{7}$
$⇒63x = 45x + 54$
$⇒18x = 54$
$⇒x = 3$
So, the quantity of milk in the mixture is $9x = 9×3 = 27$
Hence, the correct answer is 27 litres.
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