Yeah!! Artificial Series is back Again (again(again))

The solution you started with was 15% alcohol. That means the solution was 85% water. If you add a quantity of 100% alcohol, you are not adding any water, so the amount of water will remain unchanged. You start out with 400ml of solution. 85% of 400 is is 340ml of water. After the pure alcohol is added to make a 32% solution, you will still have 340ml of water. But this time the solution will be only 100%-32%=68% of water. 340ml water /68% = 500ml total. final - initial = 500ml-400ml= [100ml pure alcohol was added].

To strengthen 400ml 15% solution by adding x ml of 100% alcohol so as to obtain 32% ( 400+x) solution.

Rewriting, 400(15/100) + x(100/100)=32/100(400+x) => 60+x=128+ 32/100x => 68/100x= 128 => x= (128*100)/128=100 ml

Let the pure alcohol to be added be $x$ ml.

Quantity of Alcohol in 15% 400ml solution $= \dfrac{15 \times 400}{100} = 60$ ml

Total quantity of 32% Alcohol solution $= 400 + x$ ml

Quantity of alcohol in (400 + x) ml solution of 32%,

$= (400 + x) \times \dfrac{32}{100} = (128 + \dfrac{8x}{25})$

Quantity of Alcohol needed = $128 + \dfrac{8x}{25} - 60$

But $68+\dfrac{8x}{25} = x$

Solving for $x$ , we get $x= \boxed{100 ml}$