Pipe A and pipe B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than A to fill it, then the time in which A and B will fill that cistern separately will be, respectively, _____________.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 10 min and 15 min.
We know,
Work = Efficiency × Time
Now,
Let the time taken by pipe A be x
Time taken by pipe B be x + 5
According to the question;
⇒ (1/x) + (1/x + 5) = 1/6
⇒ 6(x + x + 5) = x2 + 5x
⇒ 12x + 30 = x2 + 5x
⇒ x2 - 7x - 30 = 0
⇒ x = 10 and -3
The time taken by A = x = 10 min
The time taken by B = x + 5 = 10 + 5 = 15 min