Question : Pipe A can fill an empty tank in 18 hours and Pipe B can fill the same empty tank in 24 hours. If both the pipes are opened simultaneously, how much time (in hours) will it take to fill the empty tank?
Option 1: $11 \frac{3}{7}$
Option 2: $10 \frac{1}{7}$
Option 3: $10 \frac{2}{7}$
Option 4: $11 \frac{2}{7}$
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Correct Answer: $10 \frac{2}{7}$
Solution :
Given: Pipe A can fill an empty tank in 18 hours.
Pipe B can fill the same empty tank in 24 hours.
Part filled by Pipe A in 1 hour $= \frac{1}{18}$
Part filled by Pipe B in 1 hour $= \frac{1}{24}$
If both pipes opened up simultaneously,
Part filled by A and B in 1 hour $= \frac{1}{18}+\frac{1}{24}$
⇒ $\frac{4+3}{72}=\frac{7}{72}$
Total time taken by A and B to fill the tank $= \frac{72}{7}=10\frac{2}{7}$ hours.
Hence, the correct answer is $10\frac{2}{7}$.
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