Question

A drum of water was $\frac{4}{5}$ full. When 8 bottles of water were taken out and then 6 bottles of water were poured into it, it was $\frac{3}{4}$ full. How many bottles of water can the tin contain?

Answer 1

Let the full drum capacity be p bottles of water.

Number of bottles the drum can contain $=\frac{4}{5}p$

Number of bottles of water remaining when 8 bottles of water were taken out
$=\frac{4}{5}p-8$

Number of bottles of water remaining when 6 bottles of water were added
$=\frac{4}{5}p-8+6$

Therefore,
$\frac{4}{5}p-8+6=\frac{3}{4}p$

$⟹\frac{4}{5}p-\frac{3}{4}p-2=0$

$⟹\frac{16-15}{20}p=2$

$⟹\frac{1}{20}p=2$
$⟹p=2\times 20=40$

The drum contains 40 bottles of water.