Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?

Question: Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?

Solution:
Let,
the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours

ATQ,
{1/x + 1/(x + 6)} = 1/4
⇒ (x + 6 + x)/{x(x + 6)} = 1/4
⇒ (2x + 6)/(x² + 6x) = 1/4
⇒ (x² + 6x) = 8x + 24
⇒ x² + 6x - 8x - 24 = 0
⇒ x² - 2x - 24 = 0
⇒ x² - 6x + 4x - 24 = 0
⇒ x(x - 6) + 4(x - 6) = 0
⇒ (x - 6)(x + 4) = 0
⇒ x = 6 or - 4
∴ x = 6 [neglecting the negative value of x]

∴ the cistern be filled by pipe A alone in 6 hours