Question : A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4 : 5. The quantity of alcohol in the given mixture is:
Option 1: 3 litres
Option 2: 4 litres
Option 3: 15 litres
Option 4: 10 litres
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Correct Answer: 10 litres
Solution :
Given: A mixture contains alcohol and water in the ratio 4 : 3.
Let the quantity of alcohol and water be $4x$ and $3x$, respectively.
Now, as per given conditions:
$\frac{4x}{3x+5}=\frac{4}{5}$
⇒ $20x=12x+20$
⇒ $8x=20$
⇒ $2x=5$
$\therefore$ Quantity of alcohol = $4x$ = 2 × 5 = 10 litres
Hence, the correct answer is 10 litres.
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