Question

Two pipes can fill a tank in 15 hrs and 12 hrs resp. and a third pipe can empty it in 4 hrs. If the pipes be opened at 8AM, 9AM and 11AM resp., the tank will be emptied at​

Answer 1

LCM(15,12,4)=60

Suppose capacity of the tank is 60 litre.

Amount of water filled by first pipe in 1 hr 

=6015=4=6015=4 litre.

Amount of water filled by second pipe in 1 hr 

=6012=5=6012=5 litre.

Amount of water emptied by third pipe in 1 hr 

=604=15=604=15 litre.

From 8 am to 9 am,  amount of water filled by first pipe 

=4=4 litre.

From 9 am to 11 am,  amount of water filled by first and second pipe together 

=(4+5)×2=18=(4+5)×2=18 litre.

At 11 am, quantity of water in the tank =4+18=22=4+18=22 litre.

All the pipes are open from 11 am and amount of water emptied in 1 hr

=15−(4+5)=6=15−(4+5)=6 litre.

Therefore, time required to empty the tank =226=323=226=323 hr = 3 hour 40 min

i.e., the tank will be emptied (3 hour 40 min) after 11 am.

i.e., at 2:40 pm