Correct Answer - Option 1 : 18.50
Given: Two pipes – A and B can fill a tank in 16 hours and 20 hours respectively. Both the pipes are opened. After one hour, pipe B is closed for 1 hour. Then after, pipe A is closed and B is opened for the remaining time.
Formula: If the time taken by pipes P1, P2,..Pn to fill a tank is p1, p2, ...pn and the time taken by pipes Q1, Q2, ..., Qn to empty it be q1, q2,..., qn respectively and the total time taken by all the pipes to fill the tank is t.
1/t = (1/p1 + 1/p2 + ... + 1/pn) – (1/q1 + 1/q2 + ... + 1/qn)
Efficiency is inversely proportional to time taken for doing work.
Total work = Efficiency × time
Calculation:
Let the total work be 80 units i.e., LCM of 16 and 20.
Efficiency of A = 80/16 = 5 units per hour
Efficiency of B = 80/20 = 4 units per hour
Amount of work done when both pipes open for 1 hour = (5 + 4) × 1 = 9 units
Work done by A in next 1 hour when B is closed = 5 × 1 = 5 units
Remaining work = 80 – 9 – 5 = 66 units, which has to be filled by B.
Time taken by B = 66/4 = 16.5 hour (total work/efficiency = time)
Total time to fill the tank = 1 + 1 + 16.5 = 18.5 hours
