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., respectively, on the same day. When will the tank be full?

• A. 11:20 p.m.
• B. 3:20 p.m.
• C. 7:20 p.m.
• D. 5:20 p.m.

Answer 1

Answer:

B. 3:20 p.m.

Solution: Given: A tank is filled by pipes A, B, C in 15, 30, and 40 hours respectively A, B, C are opened at 6 am , 8 am and 10 am respectively Calculation: Pipe A fill the tank in 15 hours Pipe A fill the tank in 1 hours = 1/15 Pipe B fill the tank in 30 hours Pipe B fill the tank in 1 hour = 1/30 Pipe C fill the tank in 40 hour Pipe C fill the tank in 1 hour = 1/40 Pipe A work done since it is opened at 6 am to 10 am i.e for 4 hours Then , pipe A works in 4 hours = 1/15 × 4 = 4/15 Similarly, Pipe B works done since it is opened to 8 am to 10 am i.e for 2 hours Then, pipe A works for 2 hours = 1/30 × 2 = 2/30 Total work done from 6 am to 10 am = 4/15 + 2/30 ⇒ (8 + 2)/30 = 1/3 Now, Remaining work = 1 - 1/3 = 2/3 Now , 2/3 work done by (A + B + C) together after 10 am Work done by (A + B + C)'s in 1 day = 1/15 + 1/30 + 1/40 ⇒ (8 + 4 + 3)/120 = 15/120 = 1/8 Now , 1/8 part of work done by (A + B + C)'s in 1 hour 1 part of work done by (A + B + C)'s = 8 hours 2/3 part of work done by (A + B + C)'s = 8 × 2/3 = 16/3 hours = 5 hours 20 minutes Then , Time taken to fill the tank = 10 am + 5 hours 20 min = 3 : 20 pm The tank will full at 3:20 pm