A pipe can fill a tank in 30 minutes Due to two leakages A and B the filled tank would be drained of...........

Quantitative Aptitude (CPO) Pipes&cistern

A pipe can fill a tank in 30 minutes. Due to two leakages A and B, the filled tank would be drained off in $1\frac{1}{2}$ hour and $1\frac{1}{4}$ hour

respectively. How long will it take to fill the tank if the pipe, A and B are left open?

This questions was previously asked in

SSC CPO 15th-March-2019-Shift-1

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$1\frac{7}{8}$ $hours$

$1\frac{1}{3}$ $hours$

$1\frac{4}{5}$ $hours$

$1\frac{5}{6}$ $hours$

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Explanation:

0.5 hour will take to full tank.
So, in 1 hour it will fill 2 times of tank.
first drain will clear (2/3) part of the tank in 1 hour.
second drain will clear (4/5)part of the tank in 1 hour.
So, in 1 hour ,both the tank will clear (together) = (2/3) + (4/5) = 22/15.
part of the tank.
So, when these three open together,
the resultant part will fill in 1 hour
= 2 − (22/15) = 8/15.
So, full tank will be filled in 15/8 hours.
So, Option A is correct.