Question

$8$ litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in the cask to that of the water is $16:65.$ How much wine did the cask hold originally?

• A. $18$ litres
• B. $24$ litres
• C. $32$ litres
• D. $12$ litres

Answer 1

The correct option is B $24$ litres

Let the quantity of the wine in the cask originally be $x$ litres.
After first operation, wine left in the cask $=(x-8)$ litres.
So, the ratio of the quantity of wine now left in cask to that of filled cask $=\frac{x-8}{x}$
This operation is performed three more times.
Then, Wine $:$ Water $=16:65$
or, Wine $:$ Total $=16:81$
$\Rightarrow {\left(\frac{x-8}{x}\right)}^4=\frac{16}{81}$
$\Rightarrow \frac{x-8}{x}=\frac{2}{3}$
$\Rightarrow 3x-24=2x$
$\Rightarrow x=24$ litres