Question : Pipes A and B can fill a tank in 18 minutes and $22 \frac{1}{2}$ minutes, respectively while pipe C can empty the full tank in 12 minutes. A and B are opened together for 6 minutes and then closed. Now C is opened. C alone will empty the tank in ____.
Option 1: $5$ minutes
Option 2: $8 \frac{2}{5}$ minutes
Option 3: $7 \frac{1}{5}$ minutes
Option 4: $6$ minutes
Correct Answer: $7 \frac{1}{5}$ minutes
Solution :
$22\frac12=\frac{45}{2}$
Total work LCM of 18, $\frac{45}{2}$, and 12 = 180 units
Work done by pipe A and pipe B in 6 min = (10 + 8) × 6 = 108
Pipe C alone empty the tank filled by pipe A and pipe B in 6 min = $\frac{108}{15}$
⇒ $7\frac15$ minutes
Hence, the correct answer is $7\frac15$ minutes.
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