Four pipes can fill a tank in 15, 20, 30 and 60 hours respectively. The first pipe was opened at 8 a.m, second at 9 a.m, third at 10 a.m. and fourth at 11 a.m. When will the tank be full-

Question: Four pipes can fill a tank in 15, 20, 30 and 60 hours respectively. The first pipe was opened at 8 a.m, second at 9 a.m, third at 10 a.m. and fourth at 11 a.m. When will the tank be full-

Solution:
Let,
the time be x hours after 8 am.
Then, the first pipe worked for x hours
Second pipe for (x - 1) hours;
Third pipe for (x - 2) hours;
Fourth pipe for (x - 3) hours.

ATQ,
(x/15) + {(x - 1)/20} + {(x - 2)/30} + {(x - 3)/60} = 1
⇒ (4x + 3x - 3 + 2x - 4 + x - 3)/60 = 1
⇒ 10x - 10 = 60
⇒ 10x = 70
∴ x = 7

So, the tank will be full 7 hours after 8 am = 8 + 7 = 15 = 3 p.m.