Question

Milk contains $5\%$ water What quantity of pure milk should be added to $10$ litres of milk to reduce this to $2\%$.

• A. $5liters$
• B. $7liters$
• C. $11liters$
• D. $15liters$

Answer 1

Answer: (D)

$15liters$

Initially $5\%$ is the portion of the water in the mixture, $95\%$ is the portion of the milk in the mixture.

So quantity of water(in litres) in the $10$ litres $=\frac{5}{100}\times 10$ litres $=0.5$ litres

And also quantity of milk in $10$ L mixture $=\frac{95}{100}\times 10$ L $=9.5$ L

Let $X$ be the quantity of pure milk to be added to the mixture to make water content to $2\%$.

$\therefore$ $\frac{0.5}{(9.5+x)}\times 100=\frac{0.2}{9.8}\times 100$

$\Rightarrow 9.8\times 0.5=0.2(9.5+x)$

$\Rightarrow 4.9=1.9+0.2x$

$\Rightarrow 0.2x=3.0$

$\Rightarrow x=15$

So, $15$ liters of pure milk should be added to the mixture to reduce the water content to $2\%$