A takes 6 days less than the time taken by B to finish a piece of work. If both A And B together can finish it in 4 days, find the time taken by B to finish the work.

$Step -1: Finding the work done by A and B in a day .$

$Let B takes a total of x days to complete the work alone .$

$So as know that A takes 6 days less than B we can write that A takes$

$x - 6 days to complete the work alone .$

$Work done by B in a day = \frac{1}{x}$

$Work done by A in a day = \frac{1}{x - 6}$

$Step -2: Finding x .$

$As we know that A and B together complete the work in 4 days,we can write$

$\frac{1}{x} + \frac{1}{x - 6} = \frac{1}{4}$

$Taking LCM and solving we get,$

$\frac{x - 6 + x}{x ( x - 6 )} = \frac{1}{4}$

$\frac{2 x - 6}{x ( x - 6 )} = 4$