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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