Question : Pipes A and B can fill a tank in 36 hours and 48 hours, respectively. Both pipes are opened together for 9 hours and then A is closed. Pipe B alone will fill the remaining part of the tank now in:
Option 1: $20 \frac{1}{2}$ hours
Option 2: $25$ hours
Option 3: $27$ hours
Option 4: $24$ hours
Correct Answer: $27$ hours
Solution :
Given: Pipes A and B can fill a tank in 36 hours and 48 hours, respectively.
Both pipes are opened together for 9 hours and then A is closed.
Let the total work be 144 units. (LCM of 36 and 48)
So, the efficiency of A $=\frac{144}{36}=$ 4
and the efficiency of B $=\frac{144}{48}=$ 3
The work completed in 9 hours by pipes A and B $=(4 + 3) \times 9 = 63$ units
The work left = 144 – 63 = 81 units
The time required to complete the remaining work by Pipe B alone $=\frac{81}{3}=27$ hours
Hence, the correct answer is $27$ hours.
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