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, how many days will B take to finish the work?

We will use the concept of work done to solve this question.

Answer: 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, then B takes 12 days to finish the work.

Let's assume B takes x days to finish the work. We get the quadratic equation in terms of x and we will solve the equation.

Explanation:

Suppose B alone takes x days to finish the work. Then A alone can finish it in (x−6) days

Now A's one day's work + B's one day's work = 1/x ​+ 1/(x - 6)​ and (A + B)'s one day's work = 1/4

1/x ​+ 1/(x - 6)​ = 1/4

⇒(x − 6) + x / x(x - 6) ​= 1/4 ​

⇒ (2x - 6)/(x² - 6x) = 1/4

⇒ 4(2x - 6) = 1(x² - 6x) 

⇒8x − 24 = x² − 6x

⇒x² − 14x + 24 = 0

⇒x² − 12x − 2x + 24 = 0

⇒(x − 12) (x - 2) = 0

⇒x = 12 or x = 2, but x cannot be less than 6.

So,  x = 12

Therefore, B can finish the work in 12 days.