Question
Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If A is open all the time and B and C are open for one hour each alternately, the tank will be full in :
Answer: Option C
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(A + B)'s 1 hour's work = `(1/12 + 1/15) = 9/60 = 3/20`.
(A + C)'s 1 hour's work = `(1/12 + 1/20) = 8/60 = 2/15`.
part filled in 2 hrs. = `(3/20 + 2/15) = 17/60` .
part filled in 6 hrs. = `(3 xx 17/60) = 17/20`.
Remaining part = `(1 - 17/20) = 3/20`.
Now, it is the turn of A and B `3/20` part is filled by A and B in 1 hour.
`:.` Total time taken to fill the tank = (6 +1) hrs. = 7 hrs.
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