Question

A tank is lled by three pipes with uniform ow. The rst two pipes operating simultaneously ll the tank in the same time during which the tank is lled by the third pipe alone. The second pipe lls the tank 5 hours faster than the rst pipe and 4 hours slower than the third pipe. The time required by the rst pipe is:

Answer 1

A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank at the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:

Given,

Pipe P1 → T1 = T  

Pipe P2 → T2 = T-5 and T2 = T3 + 4

Pipe P3 → T3 = T2-4 = T-5-4 = T - 9  

Using the substitution method, we get,  

Time is taken by pipe to fill the tank,

T1 = T = 15 hr  

T2 = 10 hr

T3 = 6hr  

from the above result obtained we can say that,

The pipe P1 fills the tank 40% in 15 hours & P2 fills the tank 60% in 10 hours and P3 fills the tank 100% in 6 hours.

Therefore first pipe P1 takes 15 hr to fill the tank alone.