Question : Pipes A and B can fill a tank in 16 hours and 24 hours, respectively, whereas pipe C can empty the full tank in 40 hours. All three pipes are opened together, but pipe A is closed after 10 hours. After how many hours will the remaining part of the tank be filled?
Option 1: $12 \frac{1}{2}$
Option 2: $10$
Option 3: $20$
Option 4: $15\frac{1}{2}$
Correct Answer: $12 \frac{1}{2}$
Solution :
Pipe A can fill in 1 hour = $\frac{1}{16}$
Pipe B can fill in 1 hour = $\frac{1}{24}$
Pipe C can empty in 1 hour = $\frac{1}{40}$
Together they can fill in 1 hour $=\frac{1}{16} + \frac{1}{24} – \frac{1}{40}=\frac{19}{240}$
Together they can fill in 10 hours = $10\times\frac{19}{240}=\frac{19}{24}$
$\therefore$ Remaining tank = $1-\frac{19}{24}=\frac{5}{24}$
B and C can do in 1 hours = $\frac{1}{24} – \frac{1}{40}=\frac{2}{120}=\frac{1}{60}$
B and C can fill a tank in 60 hours.
$\therefore$ B and C can fill $\frac{5}{24}$th tank = $60 × \frac{5}{24}=\frac{25}{2}=12\frac{1}{2}$ hours
Hence, the correct answer is $12\frac{1}{2}$ hours.
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