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Pipe A fills a tank of capacity 700 liters at the rate of 40 liters a minute. Another pipe, pipe B, fills the same tank at the rate of 30 liters a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute. If pipe A is kept open for a minute and then closed and pipe B is kept open for a minute and then closed and then pipe C is kept open for a minute and then closed and the cycle repeated, when will the tank be full?
A) 46 minutes 40 seconds
B) 52 minutes 15 seconds
C) 40 minutes 20 seconds
D) 36 minutes 50 seconds
Correct answer:
C) 40 minutes 20 seconds
Description for Correct answer:
Pipe A fills the tank at the rate of 40 liters a minute, pipe B at the rate of 30 liters a minute and pipe C drain the tank at the rate of 20 liters a minute.
lf each of them is kept open for a minute in the order A+B-C, then the tank will have 50 liters of water at the end of 3 minutes.
After 13 such cycles, the tank will have \( \Large 13 \times 50 \) = 650 litres of water.
It will take \( \Large 13 \times 3 \) = 39 minutes for the 13 cycles to be completed.
At the end of the 29th minute, Pipe C will be closed and pipe A will be opened.
Pipe A will add 40 more liters to the tank.
Therefore, at the end of the 40th minute, the tank will have 650 + 40 = 690 liters of water.
At the end of the 40th minute, Pipe A will be closed and Pipe B will be opened.
Pipe B will add 30 liters of water in a minute. Therefore, at the end of the 41st minute, the tank will have 690 + 30 = 720 liters of water.
But as the capacity of the tank is only 700 liters, the tank will overflow before Pipe B can complete its 14th cycle. Therefore, Pipe B need not be kept open for a full minute at the end of 40 minutes.
Pipe B needs to add just 10 more liters of water at the end of 40 minutes for which it will take 1/3rd of a minute.
Therefore, the total time taken for the tank to overflow
= 40 minutes + 1/3 of a minute or 40 minutes 20 seconds.
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