Two pipes A and B can fill a tank in 18 and 24 minutes respectively. After both are opened together for 6 minutes, the rate of pipe A becomes half, and pipe B becomes double its original. In how many more minutes will the tank be full?

Correct option is A

Given:
Pipe A can fill the tank in 18 minutes.
Pipe B can fill the tank in 24 minutes.
Both pipes are opened together for 6 minutes.
After 6 minutes, the rate of pipe A becomes half and pipe B becomes double.
Formula Used:
Work = Rate × Time
Rate = Total Work ÷ Time
Solution :
LCM of 18 and 24 = 72 units (Total Work)
Initial Efficiency of Pipe A = 72 ÷ 18 = 4 units/min
Initial Efficiency of Pipe B = 72 ÷ 24 = 3 units/min
Work done together in 1 minute = 4 + 3 = 7 units
Work done in first 6 minutes = 6 × 7 = 42 units
Remaining work = 72 − 42 = 30 units
After 6 minutes (changed efficiency):
New rate of pipe A = 4 ÷ 2 = 2 units/min
New rate of pipe B = 3 × 2 = 6 units/min
New combined rate = 2 + 6 = 8 units/min
Time to complete remaining work = 30 ÷ 8 = 3.75 minutes