Management Aptitude Test Sep 2013 Paper

Question : 84 of 200

Marks: +1, -0

There are three pipes, A, B and C, opening into a tank. Each pipe can be used to fill or empty the tank at the same respective rate. The ratio of the rates of the three pipes at, which they either fill or empty the tank is 2:3 :4. Pipes A and B, working together, take 3 h to fill the tank when both are used as inlet pipes. In the first, second and third hours of operation, the pipes, A, B and C respectively are used as emptying pipes, while the other two pipes are used as filling pipes. What is the fraction of the tank to be filled at the end of the three hours ?

$1/5$
$3/5$
$2/5$
$4/5$

Validate

Solution:

(c) Let the common ratio be x.
Since, pipe A takes 2x h to fill or to empty the tank.
Pipe B takes 3x h to fill or to empty the tank.
Pipe C takes 4x h to fill or to empty the tank.
Now, Pipe A and B can fill the tank in 3 h
∴ =

1/{2x}+1/{3x}=1/3

{3+2}/{6x}=1/3

x =

{5×3}/6=5/2

So, pipe A, B and C simultaneously take 5h, 7.5 h and 10 h to fill or to empty the tank.
Now, by given condition,

(1/5+1/7.5-1/10)

( 1/7.5+1/10-1/5)

(1/10+1/5-1/7.5)

({6+4-3}/30)

({4+3-6}/30)

({3+6-4}/30)

7/30+1/30+5/30

13/30=2/5

Hence, after 3 h tank is

2/5

filled

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