Question : A tank can be filled by pipe A in 2 hours and by pipe B in 6 hours. At 10 A.M., pipe A was opened. At what time will the tank be filled if pipe B is opened at 11 A.M.?
Option 1: 12.45 A.M.
Option 2: 5 P.M.
Option 3: 11.45 A.M.
Option 4: 12 P.M.
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Correct Answer: 11.45 A.M.
Solution :
Given: A tank can be filled by pipe A in 2 hours and by pipe B in 6 hours.
Assume the tank's capacity is 6 units. (Least common
multiple
of 2 and 6)
Efficiency of a pipe = $\frac{\text{capacity of the tank}}{\text{time taken by the pipe}}$
⇒ Efficiency of pipe A = $\frac{6}{2}$ = 3 and Efficiency of pipe B = $\frac{6}{6}$ = 1
Pipe A was opened at 10 am and pipe B was opened at 11 A.M.
Units of water filled by A in 1 hour (10 A.M. to 11 A.M.) = 3 units
⇒ Remaining units of water to be filled = 6 – 3 = 3 units
So, the time will be taken by pipe A and pipe B to fill the remaining tank = ($\frac{3}{3+1}$) × 60 = 45 minutes
So, the tank will be filled at 11:45 A.M.
Hence, the correct answer is 11:45 A.M.
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