Pipe A can fill an empty tank in 6 hours and pipe B in 8 hours. If both the pipes are opened and after 2 hours pipe A is closed, how much time B will take to fill the remaining tank?

Pipe A can fill an empty tank in 6 hours and pipe B in 8 hours. If both the pipes are opened and after 2 hours pipe A is closed, how much time B will take to fill the remaining tank?
[A]2\tfrac{1}{3}\ hours
[B]3\tfrac{1}{3}\ hours
[C]2\tfrac{2}{5}\ hours
[D]7\tfrac{1}{2}\ hours

3\tfrac{1}{3}\ hours
Part of the tank filled by pipe A and B in 2 hours
= 2\left ( \frac{1}{6}+\frac{1}{8} \right )
= 2\left ( \frac{4+3}{24} \right ) = \frac{7}{12}
Remaining part = 1-\frac{7}{12} = \frac{5}{12}
This part is filled by pipe B.
∴ Required Time = \frac{5}{12}\times 8 = \frac{10}{3} = 3\frac{1}{3}\ hours
Hence option [B] is correct answer.

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