Three taps P Q and R can fill a tank in 10 20 and 30hours respectively If P is open all the time and...........

Quantitative Aptitude ( CCS) Pipes&cistern

Three taps P,Q and R can fill a tank in 10,20 and 30hours respectively. If P is open all the time and Q and R are open for one hour each alternately, then the tank will be full in

6 hours

6.5 hours

7 hours

7.5 hours

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Explanation:

(P+Q)’s 1 hour’s work = (1/10+1/20) = 3/20
(A+C)’s 1 hour’s work = (1/10+1/30) = 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 P and Q and 3/20 part is filled by P and Q in 1 hour.
Therefore, Total time taken to fill the tank = (6+1) hrs = 7 hrs