When operated seprately , pipe A takes 5 hours less than pipe B to fill a cistern, and when both pipes are operated together , the cistern gets filled in 6 hours. In how much time ( in hours) will pipe B fill the cistern , if operated separately ?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 15
Let's assume time taken by Pipe A = X - 5
Time taken by Pipe B = X
They can together fill a cistern = 6 days
So, their one day work
1/(X - 5) + 1/X = 1/6
(X + X - 5)/(X2 - 5X) = 1/6
12X - 30 = X2 - 5X
X2 - 17X + 30 = 0
X2 - 15X - 2X + 30 = 0
X(X - 15) - 2(X - 15) = 0
(X - 15) (X - 2) = 0
X = 2 Can't possible
X = 15
So, pipe B will fill the tank in X = 15 days.