Pipe A can fill a cistern in 6 hours and pipe B can fill it in 8 hours.
Question:

Pipe A can fill a cistern in 6 hours and pipe B can fill it in 8 hours. Both the pipes are opened and after two hours, pipe A is closed. How much time will B take to fill the remaining part of the tank?

Solution:

Pipe A can fill a cistern in 6 hours.

Pipe B can fill a cistern in 8 hours.

Part of the cistern filled by pipe A in one hour $=\frac{1}{6}$

Part of the cistern filled by pipe B in one hour $=\frac{1}{8}$

Part of the cistern filled by pipes A and B in one hour $=\frac{1}{6}+\frac{1}{8}=\frac{4+3}{24}=\frac{7}{24}$

Part of the cistern filled by pipes A and B in 2 hours $=\frac{7}{24} \times 2=\frac{7}{12}$

Part of the tank empty after 2 hours $=1-\frac{7}{12}=\frac{5}{12}$

Time taken by pipe B to fill the remaining tank $=\frac{5}{12} \div \frac{1}{8}=\frac{5}{12} \times 8=\frac{10}{3}=3 \frac{1}{3}$ hours

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