Question : Pipe A can fill an empty tank in 6 hours and pipe B, in 8 hours. If both pipes are opened and after 2 hours, pipe A is closed, how much time will B take to fill the remaining tank?
Option 1: $7\frac{1}{2}$ hours
Option 2: $2\frac{2}{5}$ hours
Option 3: $2\frac{1}{3}$ hours
Option 4: $3\frac{1}{3}$ hours
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Correct Answer: $3\frac{1}{3}$ hours
Solution :
Given: Pipe A can fill an empty tank in 6 hours and pipe B, in 8 hours.
So, in 1 hour, pipe A can fill $\frac{1}{6}$ part and pipe B can fill $\frac{1}{8}$ part of the tank separately.
In 1 hour, both pipes together can fill ($\frac{1}{6}$+$\frac{1}{8}$) = $\frac{7}{24}$ part of the tank.
Now, in 2 hours, they can fill ($\frac{7}{24}$ × 2) = $\frac{7}{12}$ part of the tank.
So, the part of the tank still empty is (1 – $\frac{7}{12}$) = $\frac{5}{12}$
Now, pipe B can fill 1 part of the tank in 8 hours.
So, pipe B can fill the remaining $\frac{5}{12}$ part of the tank in (8 × $\frac{5}{12}$) = $\frac{10}{3}$ hours
Therefore, to fill the remaining tank, pipe B will take $\frac{10}{3}$ hours = $3\frac{1}{3}$ hours
Hence, the correct answer is $3\frac{1}{3}$ hours.
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