Question 29

A vessel of capacity V liters can be filled by two taps A and B independently in $$\frac{1}{4}$$ hr and $$\frac{1}{6}$$ hr respectively. A tap C empties the full tank at the rate of 7 liters per min. If all the 3 taps are opened simultaneously, the full vessel is emptied in 120 min. Then V =

Solution

A can fill tank in(1/4)hr=15 min.

and B can fill tank in (1/6)hr=10 min.

C can empty the 7 litter in 1 min.

So, in 1 min A can fill V/15 part of tank.

in 1 min B can fill V/10 part of tank.

1 min A,B and C can empty (7-V/15-V/10)

=(210-5V)/30.

=(42-V)/6.

=(7-V/6).

in 120 min it will empty (840-20V).

So, (840-20V)=V.

or,21V=840.

or,V=40.

So,D is correct choice.

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