Question

 A cistern can be filled by two taps A and B in 12 hours and 16 hours respectively. The full cistern can be emptied by a third tap C in 8 hours. If all the taps are turned on at the same time, in how much time will the empty cistern be filled completely?

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Answer 1

Answer:

Step-by-step explanation:

tap A to fill the cistern = 12 hours.

tap B to fill the cistern = 16 hours.

tap C to empty the full cistern = 8 hours.

A’s 1 hour’s work = ¹/₁₂

B’s 1 hour’s work = ¹/₁₆

C’s 1 hour’s work = −1/9 (cistern being emptied by C)

(A + B + C)’s 1 hours net work= (¹/₁₂ + ¹/₁₆ - ¹/₈) = ¹/₄₈

time taken by (A + B + C) to fill the cistern = 48 hours.

Answer 2

Answer:

1/12+1/16+1/8

=1/48

time taken by ABC to filled completely=1/1/48

=48/1

=48hours