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

A
18
CORRECT ANSWER WRONG ANSWER
B
36
CORRECT ANSWER WRONG ANSWER
C
27
CORRECT ANSWER WRONG ANSWER
D
24
CORRECT ANSWER WRONG ANSWER
Solution

Correct option is

(D)

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