Question

A tank is emptied by 2 pipes and filled by a third. If the 1st two can empty the tank in 2 and 3 hrs respectively and third can fill it in 4 hours, the time taken to empty the tank ${\left(\frac{4}{5}\right)}^{th}$ full when all three are open is p/35,what is the value of p.

Answer 1

Let the time taken to completely empty the tank is x hrs $\frac{1}{x}=\frac{1}{2}+\frac{1}{3}+(-\frac{1}{4})$
$\Rightarrow \frac{1}{x}=\frac{7}{12}\Rightarrow x=\frac{12}{7}$ hrs
Complete tank will be emptied in $\frac{12}{7}$ hrs
$\therefore {\left(\frac{4}{5}\right)}^{th}$ tank will be emptied in
= $\frac{12}{7}\times \frac{4}{5}=\frac{48}{35}$ hrs