Question

Two pipes A and B can fill a tank in 4 hours and 5 hours respectively If the pipes A and B are turned on alternately for 1 hour each then what is the time taken to fill the tank ?

• A. $2\frac{2}{5}$ hours
• B. $3\frac{2}{5}$ hours
• C. $4\frac{2}{5}$ hours
• D. $5\frac{2}{5}$ hours

Answer 1

The correct option is C $4\frac{2}{5}$ hours

When the wo pipes are opened alternately for one hour each part of the tank filled by them in 2 hours = $\frac{1}{4}+\frac{1}{5}=\frac{9}{20}$
$\therefore$ Part of the tank filled in 4 hours = $\frac{9}{10}$
Remaining part $=1-\frac{9}{10}=\frac{1}{10}$
Thus $\frac{1}{10}th$ of the tank has to be filled by pipe A in $\frac{4}{10}=\frac{2}{5}$ hours (since in the 5th hour it is pipe A's turn)
$\therefore$ The whole tank can be filled in $4\frac{2}{5}$ hours