Question

A pharmacist needs to strengthen a $10\%$ alcohol solution to one of $20\%$ alcohol.How much pure alcohol should be added to $400$ml of $10\%$ solution?

Answer 1

Let $x$ ml of pure alcohol be added to $400$ml of $10\%$ solution to convert, it into $20\%$ alcohol.

In $10\%$ alcohol,pure alcohol in $400$ml$=\frac{400\times 10}{100}=40$ml

To be added in the solution of $400$ml$=x$ml

In $20\%$ alcohol,pure alcohol in $400+x$ml$=\frac{(400+x)\times 20}{100}$

$\Rightarrow 40+x=\frac{(400+x)\times 20}{100}$

$\Rightarrow 40+x=\frac{(400+x)}{5}$

$\Rightarrow 200+5x=400+x$

$\Rightarrow 5x-x=400-200$

$\Rightarrow 4x=200$

$\Rightarrow x=\frac{200}{4}=50$ml

Pure alcohol to be added is $50$ml