Three pipes A, B and C are connected to a tank. A and B can fill it in 60 and 75 minutes respectively, while C can empty it in 100 minutes. If A, B and C are kept open successively for 1 minute each, how soon will the tank be filled?
Solution
Correct Answer: Option E
Pipe A’s one minute's work = 1/60
Pipe B’s one minute's work = 1/75
Pipe C’s one minute's work = -1/100 ( minus sign indicates that pipe C empties tank)
(A + B + C)’s three minute's work = 1/60 + 1/75 – 1/100 = 6/300
= 1/50
Hence, in 49 × 3 minutes, (49/50)th part will be filled. Hence, remaining part = 1/50
In next one minute, A will fill 1/60 part, hence, remaining part = 1/50 - 1/60 = 1/300.
Next, the pipe B will be opened, which will take 75/300 = 1/4 minutes to fill it.
Thus, A, B and C will together take 49 × 3 + 1 + 1/4 = 148.25 minutes.
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