Question : In a solution of water and milk, the quantity of milk is double the quantity of water. To pass the quality standards, the solution must contain 90% milk in it. If the volume of the solution is ${v}$, then how much pure milk in litres is to be added to the solution to pass the quality standard?
Option 1: $\frac{4v}{3}$
Option 2: $\frac{3v}{4}$
Option 3: $\frac{7v}{4}$
Option 4: $\frac{7v}{3}$
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Correct Answer: $\frac{7v}{3}$
Solution :
Let the volume of water in the solution as $w$ and the volume of milk as $m$.
The quantity of milk is double the quantity of water,
$\therefore m = 2w$
The total volume of the solution is $v$,
$⇒v = w + m = w + 2w = 3w$
To pass the quality standards, the solution must contain 90% milk. This means that the volume of milk after adding $x$ litres of pure milk should be $0.9(v + x)$.
$⇒m + x = 0.9(v + x)$
Substituting $m = 2w$ and $v = 3w$ into the equation,
$⇒2w + x = 0.9(3w + x)$
$⇒x = \frac{0.7w}{0.1} = 7w$
Since $w = \frac{v}{3}$,
$⇒x = 7 \times \frac{v}{3} = \frac{7v}{3}$
Hence, the correct answer is $\frac{7v}{3}$.
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