Question

Two pipes a and b can fill a tank with water in 30 minutes and 45 minutes respectively. the third pipe c can empty the tank in 36 minutes. first a and b are opened. after 12 minutes c is opened. total time (in minutes) in which the tank will be filled up is:

Answer 1

Heya

Time taken by pipe A to fill the tank = 30min

Part of tank filled in one minute = 1/30

Time taken by pipe B to fill.the tank = 45min

Part of tank filled in one.minute = 1/45

Part of tank filled in one minute by both A and B is 1/30+1/45

= (3+2)/90

= 5/90

= 1/18

In 18minutes the tank gets filled by A and B

Time taken by pipe C to empty the tank is 36min

Part of tank emptied by pipe C in one minute = 1/36

Part of tank filled when A and B fill the tank and C empties it in one.minute is

= 1/18-1/36

=(2-1)/36

= 1/36

For the first 12 minutes, only pipe A and B are opened

Part of tank filled in 12 minutes = 12×1/18=2/3

1/3 of the tank is to be filled.

1/3= time taken×1/36

36/3 = 12minutes

Total time taken = 12+12=24minutes