Question : Two pipes A and B can fill a tank in 6 hours and 8 hours respectively. If both the pipes are opened together, after how many hours should B be closed so that the tank is full in 4 hours?
Option 1: $\frac{2}{3}$ hours
Option 2: $1$ hour
Option 3: $2$ hours
Option 4: $\frac{8}{3}$ hours
Correct Answer: $\frac{8}{3}$ hours
Solution : Pipe A takes 6 hours. Pipe B takes 8 hours. LCM of 6 and 8 = 24, i.e, capacity of the tank = 24 units The efficiency of A in 1 hour $= \frac{24}{6} = 4$ units The efficiency of B in 1 hour $= \frac{24}{8} = 3$ units Pipe A works for 4 hours at an efficiency of 4 units in 1 hour = 4 × 4 = 16 units The remaining tank is filled by pipe B with an efficiency of 3 units per hour $= \frac{24–16}{3}=\frac{8}{3}$ hours Thus, pipe B should be closed after $\frac{8}{3}$ hours so that the tank is full in 4 hours. Hence, the correct answer is $\frac{8}{3}$ hours.
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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 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: $12$
Question : Two pipes, A and B, can fill a tank in 15 hours and 18 hours, respectively. Both pipes are opened simultaneously to fill the tank. In how many hours will the empty tank be filled?
Option 1: $8 \frac{2}{11}$
Option 2: $9 \frac{2}{11}$
Option 3: $7 \frac{2}{11}$
Option 4: $10 \frac{2}{11}$
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 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: $5$
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