There are three taps A, B and C in a container. Tap A and B can fill the container in 15 and 10 minutes respectively, if they are working alone. Tap C can empty it in 12 minutes if it is working alone. Initially all the Taps are closed. Tap A is opened alone for 3 minutes. Now A is closed and B is opened alone for 2 minutes. Now B is closed and C is opened alone for 5 minutes. Finally all the three taps are opened together. How long will it take to fill the tank?
10 minutes
12 minutes
Tank Cannot be filled
None of these
Answer :12 minutes
Solution (Fast Approach)
Part 1
Tap A alone can fill 100% of the container in 15 min.
Its opened for 3 minutes. Hence it fills (3/15)x100 = 20% of the conatainer
In the same way in 2 minute B can fill (2/10)x100 = 20%.
Now container is 40% full
Now Tap C is opened for 5 min. It can empty (5/12)x100 = 41.67% of the container in 5 min. Only 40% of the container is filled, hence C will completely empty the container.
Part 2
In 1 min A, B and C combined can fill (1/15 + 1/10 - 1/12) = 1/12 portion of the container
Hence 1 portion (Full) can be filled in 1/(1/12) = 12 minutes
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