Question : Two pipes, A and B, can fill a tank in 15 hours and 18 hours, respectively. Both pipes are opened simultaneously to fill the tank. In how many hours will the empty tank be filled?
Option 1: $8 \frac{2}{11}$
Option 2: $9 \frac{2}{11}$
Option 3: $7 \frac{2}{11}$
Option 4: $10 \frac{2}{11}$
Correct Answer: $8 \frac{2}{11}$
Solution :
Work done by pipe A in an hour = $\frac{1}{15}$
Work done by pipe B in an hour = $\frac{1}{18}$
Work done by pipes A and B in an hour $=\frac{1}{15}+\frac{1}{18}=\frac{6+5}{90}=\frac{11}{90}$
Therefore, the empty tank will be filled in $\frac{90}{11}$ hours
= $8\frac{2}{11}$ hours
Hence, the correct answer is $8\frac{2}{11}$.
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