Question : Pipes A and B can empty a full tank in 18 hours and 24 hours, respectively. Pipe C alone can fill the tank in 36 hours. If the tank is $\frac{5}{6}$ full and all the three pipes are opened together, then in how many hours will the tank be emptied?
Option 1: $10 \frac{1}{2}$
Option 2: $12 \frac{1}{2}$
Option 3: $10$
Option 4: $12$
Correct Answer: $12$
Solution : Time taken by pipe A to empty a full tank = 18 hr Part of tank emptied by pipe A in an hour = $\frac{1}{18}$ Time taken by pipe B to empty a full tank = 24 hr Part of tank emptied by pipe B in an hour = $\frac{1}{24}$ Time taken by pipe C to fill a full tank = 36 hr Part of tank filled by pipe C in an hour = $\frac{1}{36}$ Part of the tank emptied by pipes A, B, and C in an hour = $\frac{1}{18}+\frac{1}{24}-\frac{1}{36}$ = $\frac{4+3-2}{72}$ = $\frac{5}{72}$ Time taken by pipes A, B and C to empty the tank = $\frac{72}{5}$ hr So, the time taken by pipes A, B, and C to empty $\frac{5}{6}$th of the tank = $\frac{5}{6}×\frac{72}{5}$ = $\frac{72}{6}$ = 12 hours Hence, the correct answer is $12$.
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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: $15\frac{1}{2}$
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: $5$
Question : Pipes A and B can fill an empty tank in 6 and 8 hours respectively, while pipe C can empty the full tank in 10 hours. If all three pipes are opened together, then the tank will get filled in:
Option 1: $4 \frac{4}{23}$ hours
Option 2: $6\frac{1}{5}$ hours
Option 3: $5\frac{5}{23}$ hours
Option 4: $7\frac{1}{2}$ hours
Question : Pipes A and B can fill a tank in 36 hours and 48 hours, respectively. Both pipes are opened together for 9 hours and then A is closed. Pipe B alone will fill the remaining part of the tank now in:
Option 1: $20 \frac{1}{2}$ hours
Option 2: $25$ hours
Option 3: $27$ hours
Option 4: $24$ hours
Question : Pipes A, B and C can fill an empty tank in $\frac{30}{7}$ hours if all three pipes are opened simultaneously. A and B are filling pipes and C is an emptying pipe. Pipe A can fill the tank in 15 hours and pipe C can empty it in 12 hours. In how much time (in hours) can pipe B alone fill the empty tank?
Option 1: 3
Option 2: 5
Option 3: 6
Option 4: 4
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