Question : Taps A and B can fill a tank in 15 minutes and 10 minutes, respectively while tap C can empty the full tank in x minutes. If all three taps are opened together, the tank is filled completely in 8 minutes. Tap C alone will empty $\frac{3}{8}$ th part of the tank in:
Option 1: 10 minutes
Option 2: $10 \frac{1}{2}$ minutes
Option 3: 9 minutes
Option 4: $8 \frac{1}{2}$ minutes
Correct Answer: 9 minutes
Solution :
A can fill the tank in one minute = $\frac{1}{15}$ part of the tank
B can fill the tank in one minute = $\frac{1}{10}$ part of the tank
Let tap C can empty the tank in $x$ minutes.
C can empty the tank in one minute = $\frac{1}{x}$ part of the tank
If all the taps are opened together, the tank is filled in 8 minutes.
According to the question,
⇒ $\frac{1}{15}+\frac{1}{10}-\frac{1}{x}=\frac{1}{8}$
⇒ $\frac{1}{15}+\frac{1}{10}-\frac{1}{8}=\frac{1}{x}$
⇒ $\frac{8+12-15}{120}=\frac{1}{x}$
⇒ $\frac{5}{120}=\frac{1}{x}$
⇒ $x=24$
Thus, $x$ can empty the tank in 24 minutes.
Tap C alone will empty $\frac{3}{8}$ th part of the tank in $\frac{3}{8}\times24$ = 9 minutes.
Hence, the correct answer is 9 minutes.
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