Question

A cistern can be filled by two taps A and B in 5 hours and 10 hours, respectively. it can be emptied bi a third tap C in 20 hours. if all the tabs are turned on at the same time, in how much time will the empty cistern be filled up completely​

Answer 1

Answer:

48 hours

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.