Management Aptitude Test Dec 2019 Paper

Question : 102 of 200

Marks: +1, -0

\A

bath tube can be filled by a cold water pipe in 20 min and by a hot water pipe in 30 min. A person leaves the bathroom after turning on both pipes simultaneously and returns at the moment, when the bath tub should be full. Finding however, that the waste pipe has been open, he now closes it. In 3 min more the bath tub is full. In what time would the waste pipe empty it?

$38 {\min}$
$45 {\min}$
$43 {\min}$
$48{\min}$

Validate

Solution:

The usual time required to fill the tank when both the pipes are opened

=1 /({1}/{20}+{1}/{30})=1 / {{1}/{12}}=12 {\min}

It means work done by all the three pipes for 12 min

+

work done by both the pipes for

3 {\min}=1

Let the waste pipe takes

x

minute to empty the tank.
Then,

12[{1}/{20}+{1}/{30}-{1}/{x}]+3[{1}/{20}+{1}/{30}]=1

⇒12[{1}/{12}-{1}/{x}]+3[{1}/{12}]=1

⇒12[{x-12}/{12 x}]={3}/{4}

⇒6 x-192=12 x

⇒x=48\min

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