Three pipes P, Q and R can fill a cistern in 40 minutes, 80 minutes and 120 minutes, respectively. Initially, all the pipes are opened. After how much time (in minutes) should the pipes Q and R be turned off so that the cistern will be completely filled in just half an hour?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 12.
Let the total work = LCM of (40, 80, 120) = 240 units.
Efficiency of P = = 6 units/minute
Efficiency of Q = = 3 units/minute
Efficiency of R = = 2 units/minute
Now, let Q and R work for 't' minutes.
According to the given question,
P(30) + (Q + R)(t) = 240
⇒ 6(30) + (3 + 2)(t) = 240
⇒ 180 + 5t = 240
⇒ 5t = 60
⇒ t = 12 minutes