# Difficult Time and Work Solved QuestionAptitude Discussion

 Q. A cylindrical overhead tank is filled by two pumps $P_1$ and $P_2$. $P_1$ can fill the tank in 8 hr while $P_2$ can fill the tank in 12 hr. There is a pipe $P_3$ which can empty the tank in 8 hr. Both the pumps are opened simultaneously. The supervisor of the tank, before going out on a work, sets a timer to open $P_3$ when the tank is half filled so that the tank is exactly filled up by the time he is back. Due to technical fault $P_3$ opens when the tank is one-third filled. If the supervisor comes back as per the plan what percent of the tank is till empty?
 ✖ A. $15\%$ ✖ B. $12\%$ ✔ C. $10\%$ ✖ D. None of these

Solution:
Option(C) is correct

$P_1$ and $P_2$ can fill the tank in $\dfrac{24}{5}$ hr. [In one hour these fill $\left(\dfrac{1}{8}+\dfrac{1}{12}\right)$part of tank].

It takes $\dfrac{12}{5}$ hr in filling half the tank.

For remaining half of the tank $P_3$ will open and this will takes 6 hour.

Supervisor has gone out for $\left(\dfrac{12}{5}+6\right)$ hr.

Now, $\dfrac{1}{3}^{rd}$ tank will fill in $\dfrac{8}{5}^{rd}$  hr

In remaining $\dfrac{42}{5}$ hr only $\dfrac{33}{60}^{th}$ part of the tank will fill.

Empties part of tank

$=1-\left(\dfrac{1}{33}+\dfrac{33}{60}\right)$

$=\dfrac{1}{10}$

Which is 10% of tank.

## (4) Comment(s)

ARUN V
()

sorry for typo. it is 34/60 *

ARUN V
()

in remaining 34/5 hrs only 32/60 tank is filled. then empty tank is 1-(1/3 + 32/60) .i.e. 6/60 = 1/10. 10%

ARUN V
()

its not 1/33 it should be 1/3

RAVI KUMAR
()

HOW IS 33/60 CAME IN ABOVE SOLUTION