A tap can fill a tank in 8 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely?

Question: A tap can fill a tank in 8 hours. After half the tank is filled, two more similar taps are opened. What is the total time taken to fill the tank completely?

Solution:
Time taken by one tap to fill half the tank = 4 hrs
∴ Remaining part after 4 hrs = 1 - (1/2) = 1/2

1 pipe can fill in 1 hour = 1/8 part
Part filled by three taps in 1 hour = 3 × (1/8) = 3/8

3/8 is filled by three taps in = 1 hr
1/2 is filled by three taps in = (8/3) × (1/2) hrs
= (4/3) × 60 min = 80 min = 1 hr 20 min

So, total time taken = 4 hrs + 1 hr 20 min = 5 hrs 20 min