Three taps A B and C can fill a tank in 12 15 and 20 hours respectively If A is open all the time an...........

Quant (SSC) Pipes&cistern

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 ,C are open for one hour each alternatively, the tank will be full in:

6 hrs

20/3 hrs

7 hrs

15/2 hrs

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Explanation:

(A+B)'s 1 hour work=(1/12+1/15)=9/60=3/20
(A+C)'s 1 hour 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*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.
Therefore, Total time taken to fill the tank =(6+1)hrs= 7 hrs