Pipe and Cisterns :

1. A pipe can fill a tank in 10 hours. Find the part of tank filled in one hour.

Solution : The part of the tank filled in 1 hour = 1/10

2. A pipe can fill a tank in 56 minutes. Find the time in which 1/7 part of the tank will be filled.

Solution : We have, 1/56 part of the tank is filled in 1 minute.

∴ 1/7 part of the tank is filled in 56/7 minutes = 8 minutes.

3. A pipe can empty a cistern in 80 minutes. Find the time in which ¾ part of the cistern will be emptied.

Solution : We have, 1/80 part of the cistern is emptied in= 1 minute.

∴ ¾ part of the cistern is emptied in

= 80 × ¾ = 60 minutes.

4. A pipe can empty a cistern in 24 hours. Find the part of the cistern emptied in 4 hours.

Solution : We have, part of the cistern is emptied in 1 hour = 1/24,

∴ part of cistern emptied in 4 hours = 1/24×4=1/6

5. A tap can fill a cistern in 16 hours and another can empty it in 32 hours. If both the taps are opened simultaneously, find the time to fill the cistern.

Solution : Here, X=16 and Y=32

∴ Part of the filled in 1 hour

= 1/X − 1/Y

= 1/16 − 1/32=1/32

∴ Total time taken to fill the cistern =32 hours.