Question

Two pipes A and B can fill a tank in 24 hours and $\frac{120}{7}$ hours respectively. Harihar opened the pipes A and B to fill an empty tank and sometimes later he closed the taps A and B when the tank was supposed to be full. After that, it was found that the tank was emptied in 2.5 hours because an outlet pipe, connected to the tank was open from the beginning. If Harihar closed the pipe C instead of closing pipes A and B, the remaining tank would have been filled in :

• A. 2 hours
• B. 8 hours
• C. 6 hours
• D. 4 hours

Answer 1

The correct option is B 8 hours

Efficiency of inlet pipe $A=4.16\%\left(\frac{100}{24}\right)$
Efficiency of inlet pipe $B=5.83\%\left(\frac{100}{\frac{120}{7}}\right)$
$\therefore$ Effeciency of A and B together = 10% $\therefore$ (time = 10 hurs)
Now, if the efficiency of outlet pipe be x% then in 10 hours the capacity of tank which will be filled $=10\times (10-x)$
Now, since this amount of water is being emptied by C at x% per hour, then
$\frac{10\times (10-x)}{x}=2.5hours\Rightarrow x=8\%$
Therefore in 10 hours 20% tank is filled only. Hence, the remaining 80% of the capacity will be filled by pipes A and B in $\frac{80}{10}=8hours$.