Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tank becomes full at 10 pm. Instead, if pipe A is opened at 2 pm and pipe B is opened at 4 pm, then the tank becomes full at 6 pm. If pipe B is not opened at all, then the time, in minutes, taken to fill the tank is:
Explanation:
Let the filling and emptying capacity of A and B be ‘a’ and ‘b’ units/hour respectively.
Case 1: A is opened at 2 pm and B at 3 pm Total work done till 10 pm = 8a - 7b
Case 2: A is opened at 2 pm and B at 4 pm Total work done till 6 pm = 4a - 2b
Since work done is same in both cases, we have
8a – 7b = 4a – 2b
⇒ 4a = 5b
Now time taken by A alone to fill the tank = (Total work)/a = (4a – 2b)/a = (5b – 2b)/(5b/4) = 12/5 hours = 144 minutes.
Hence, option (c).
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