Question
Pipe A, B and C are kept open and together fill a tank in t minutes. Pipe A is kept open throughout, pipe B is kept open for the first 10 minutes and then closed. Two minutes after pipe B is closed, pipe C is opened and is kept open till the tank is full. Each pipe fills an equal share of the tank. Further more, it is known that if pipe A and B are kept open continuously, the tank would be filled completely in t minutes. How long will it take C alone to fill the tank
CAT 2021
Correct option is
Explanatory Answer :
A is kept open for all t minutes and fills one- third of the tank . Or A should be able to fill the entire tank in "3t" minutes .
A and B can together fill the tank in t minutes
A alone can fill it in 3t minutes
A and B can together can fill 1/t of the tank in a minute
A alone can fill 1/3t of the atnk in a minute
so , in a minute , B can fill 1/t - 1/3t = 2/2t
Or B takes 3t/2 minutes to fill an entire tank
to fill 1/3rd the tank , B will take t/2 minutes . B is kept open for 10 minutes
t/2 = 1- 10 , t = 20 minutes
A takes 60 minutes to fill the entire tank , while B takes 30 minutes
A is kept open for 20 minutes while B is kept open for 10 minutes
C which is kept open for 8 minutes also fills 1/3rd tank
or , we can say C alone can fill the tank in 24 minutes .
so , D is the correct option
