Discussion :: Pipes and Cistern
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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:
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Answer : Option C
Explanation :
(A + B)'s 1 hour's work =[\(\frac { 1 } {1 2 } \)+\(\frac { 1 } {1 5 } ]\) =\(\frac { 9 } {60 } \)=\(\frac { 3 } {30 } \)
(A + C)'s hour's work =[\(\frac { 1 } {1 2 } \)+\(\frac { 1 } {20 } ]\)=\(\frac {8 } {60 } \)=\(\frac { 2 } {15 } \)
Part filled in 2 hrs =[\(\frac { 3 } {30 } \)+\(\frac { 2 } {15 } \)]=\(\frac { 17 } {60 }\)
Part filled in 6 hrs =[3 x \(\frac { 17 } {60 }\)]=\(\frac { 17 } {20 }\)
Remaining part =[1-\(\frac { 17 } {20 }\)] = \(\frac { 3 } {30 } \)
Now, it is the turn of A and B and\(\frac { 3 } {30 } \)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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