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?

Options
a) 10
b) 14
c) 16
d) 12

Solution

As per question
P , Q and R work = 40 , 80 , 120
L.C.M of 40 , 80 , 120 = 240
Total work = 240
Efficiency of P = 240/40 = 6
Efficiency of Q = 240/80 = 3
Efficiency of R = 240/120 = 2
P completely filled in just half an hour now,
P(30) + (Q+R)t = 240
6 x 30 + (3 + 2)t = 240
180 + 5t = 240
5t = 240 – 180
5t = 60
t = 60/5 = 12

Ans: d) 12 minutes