Question : Pipes P and Q can fill a tank in 12 hours and 36 hours, respectively. If both pipes are opened, then how much time (in hours) will it take to fill the tank?
Option 1: 9
Option 2: 8
Option 3: 10
Option 4: 7
Correct Answer: 9
Solution :
We have,
Pipes P and Q can fill a tank in 12 hours and 36 hours.
Part filled by P in 1 hour = $\frac{1}{12}$
Part filled by Q in 1 hour = $\frac{1}{36}$
Part filled by both P and Q together in 1 hour = $\frac{1}{12}+\frac{1}{36}$ = $\frac{3+1}{36}$ = $\frac{4}{36}$ = $\frac{1}{9}$
The total time needed to fill the tank by P and Q is 9 hours.
Hence, the correct answer is 9.
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