Question : Pipes A, B, and C can fill a tank in 15, 30 and 40 hours, respectively. Pipes A, B, and C are opened at 6 a.m., 8 a.m., and 10 a.m. on the same day. When will the tank be full?
Option 1: 3:20 p.m.
Option 2: 11:20 p.m.
Option 3: 7:20 p.m.
Option 4: 5:20 p.m.
Correct Answer: 3:20 p.m.
Solution :
Let the total work = LCM of 15, 30, and 40 = 120 units
Efficiency of A =
Efficiency of B =
Efficiency of C =
According to the question,
From 6 am to 8 am, work done by A = 2 × 8 = 16 units
From 8 am to 10 am, work done by A and B = 2 × 12 = 24 units
⇒ Remaining work = 120 – 16 – 24 = 80 units, A, B and C completed together
⇒ Time taken by A, B, and C to finish the remaining work =
So, the tank fills at 10 am + 5 hours 20 minutes = 3:20 p.m.
Hence, the correct answer is 3:20 p.m.