Find the time:

Question

A large tanker can be filled by two pipes A and B in 60 mins and 40 mins respectively. How many minutes will it take to fill the empty tanker if only B is used for the first half of the time and A and B are both used in the second half of the time?

Answer 1

Part filled by pipe A in 1 minute = 1/60

Part filled by pipe B in 1 minute = 1/40

Part filled by both pipes A and pipe B in 1 minute = 1/60+1/40 = (2+3)/120 = 5/120 = 1/24

Suppose the tank is filled in x minutes

Then, To fill the tanker from empty state, B is used for x/2 minutes and 

A and B is used for the rest x/2 minutes

x/2×1/40+x/2×1/24=1

⇒x/2[1/40+1/24]=1

⇒x/2×8/120=1

⇒x/2×1/15=1

x = 15×2 = 30 minutes