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 C is closed after 10 hours. After how many hours will the remaining part of the tank be filled?
Option 1: $2 \frac{1}{2}$
Option 2: $2$
Option 3: $5 \frac{1}{2}$
Option 4: $5$
Correct Answer: $2$
Solution :
Total Work = Least Common Multiple (LCM) of 16, 24, and 40 = 240
Let the total capacity of the tank be 240 units
Efficiency of A = $\frac{240}{16}$
= 15 units
Efficiency of B = $\frac{240}{24}$
= 10 units
Efficiency of C = $\frac{240}{-40}$
= - 6 units (Since C is emptying the pipe)
When all three pipes were opened together for 10 hours,
Work done = (15 + 10 – 6) × 10 = 190 units
Remaining work = 240 units – 190 units = 50 units
Now, Pipe C is closed and the remaining tank will be filled by A and B in = $\frac{50}{(15 + 10)}$ hours.
= $\frac{50}{25}$
= 2 hours
Hence, the correct answer is $2$.
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