There are three inlet pipes, X, Y and Z, in a tank. X and Y can fill the tank in 45 hours. Y and Z can fill the tank in 36 hours. Z and X can fill the tank in 72 hours. The number of hours in which all three pipes can fill the tank, if operated simultaneously, is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 31.
x + y = 1/45 (1)
y + z = 1/36 (2)
z + x = 172 (3)
(x + y) + (y + z) + (z + x) = 1/45 + 1/36 + 1/72
So:
2(x + y + z) = (8 + 10 + 5)/360 = 23/360 ⇒ x + y + z = 23/720
Time = 1/(x + y + z) = 1/(23/720) = 720/23 ≈ 31 hours