Pipes A and B can fill a cistern in 15 hours together. But if these pipes operate separately A takes 40 hours less than B to fill the tank. In how many hours the pipe A will fill the cistern working alone?
80
70
60
50
Explanation:
Suppose B alone takes x hours to fill the cistern.
Then, A alone takes (x−40) hours to fill the cistern
$\dfrac{x(x−40)}{x+x−40}$=15
x2−40x=30x−600
x2−70x+600=0
(x−60)(x−10)=0
x=60
Suppose B alone takes x hours to fill the cistern.
Then, A alone takes (x−40) hours to fill the cistern
$\dfrac{x(x−40)}{x+x−40}$=15
x2−40x=30x−600
x2−70x+600=0
(x−60)(x−10)=0
x=60