From a container full of alcohol 6 litres of alcohol was drawn out and replaced by water. This process is repeated one more time. The ratio of the quantity of alcohol and water left in the container is 9 : 16. How many litres of alcohol did the container hold originally

15

The correct answer is option (1) : 15 litres

Let the quantity of alcohol in the container be x lit originally.

So, quantity of alcohol left in the container after 2 process of dilution $= x\left(1-\frac{6}{x}\right)^2 litre $

$∴\frac{\left(1-\frac{6}{x}\right)^2}{x}=\frac{9}{25}$

$\left(1-\frac{6}{x}\right) = \sqrt{\frac{9}{25}}$

$=1-\frac{6}{x}=\frac{3}{5}$

$\frac{6}{x}=\frac{2}{5}$

$x= 15 $

Hence, quantity of alcohol in the container was 15 litre originally.