A can do a piece of work in certain number of days. While B takes three days more than A to complete the same work. Working together, A and B can complete the work in two days. How many days does B take to complete the work?

Let, A alone can complete the whole work in x days, then
Hence, B alone can complete the whole work in = (x + 3) days

According to the question
⇒ 1/x + 1/(x + 3) = 1/2
⇒ (x + 3 + x)/x(x + 3) = 1/2
⇒ (2x + 3)/(x² + 3x) = 1/2
⇒ 4x + 6 = x² + 3x
⇒ x² - x - 6 = 0
⇒ x² - 3x - 2x - 6 = 0
⇒ x (x - 3) + 2 (x - 3) = 0
⇒ (x - 3) (x + 2) = 0

Taking,
x - 3 = 0 (x can’t be -2)
x = 3

Hence, x + 3 = 3 + 3 = 6
∴ B alone can complete the whole work in 6 days.

Short Trick:
Let, B alone can compete the whole work in 6 days
A alone can complete the whole work in = 6 - 3 = 3 days

Total work = 6
A and B together can complete the whole work in = 6/(2 + 1) = 2 days (satisfied)

So, we can say B alone can complete the whole work in 6 days.