Question : A swimming pool has 3 drain pipes. The first two pipes A and B, operating simultaneously, can empty the pool in half the time that C, the 3rd pipe, alone takes to empty it. Also pipe A, working alone, takes half the time taken by pipe B. Together they take 6 hours 40 minutes to empty the pool. The time taken by pipe A to empty the pool, (in hours) is:
Option 1: 15 hours
Option 2: 10 hours
Option 3: 30 hours
Option 4: 7 hours
Correct Answer: 15 hours
Solution :
Let the time taken by pipe B to empty the tank = $2x$ hours
Time taken by pipe A to empty the tank = $x$ hours
(A and B) takes half of the time that C takes.
⇒$\frac{2}{\frac{1}{2x}+\frac{1}{x}}=\frac{2}{\frac{1+2}{2x}}$= $\frac{4x}{3}$ hours
Pipes A, B, and C together take 6 hours and 40 minutes to empty the pool.
⇒ $\frac{1}{x}+\frac{1}{2x}+\frac{3}{4x}=\frac{1}{6+\frac{40}{60}}$
⇒ $\frac{1}{x}+\frac{1}{2x}+\frac{3}{4x}=\frac{1}{6+\frac{2}{3}}$
⇒ $\frac{4+2+3}{4x}=\frac{3}{20}$
⇒ $9×20 = 4x×3$
⇒ $x = \frac{9×20}{4×3}$
$\therefore x = 15$ hours
Hence, the correct answer is 15 hours.
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