Question

How much alcohol must be added to $400ml$ of a $15\%$ solution to make its strength $32\%$?

Answer 1

Let the required number of milliliters of alcohols be $xml$.

Given: $15\%$ of $400ml$ should be added with $100\%$ of pure alcohol.

According to the question, we have

$400\left(15\%\right)+x\left(100\%\right)=(400+x)\left(32\%\right)$

$\Rightarrow (400\times \frac{15}{100})+(x\times \frac{100}{100})=(400+x)\times \frac{32}{100}$

$\Rightarrow 60+x=128+\frac{8x}{25}$

$\Rightarrow x-\frac{8x}{25}=128-60$

$\Rightarrow \frac{17x}{25}=68$

$\Rightarrow x=\frac{68\times 25}{17}$

$\Rightarrow x=\frac{1700}{17}$

$\therefore x=100ml$

Hence, $100ml$ must be added to $400ml$ of a $15\%$ solution to make its strength $32\%$