Question

A takes 6 days less than B to do work. If both A and B working together can do it in 4 days, how many days will B take to finish it?

Answer 1

Let B alone finish the work in x days.
Therefore, A alone can finish the work in (x-6) days.
A's one day work = 1/(x-6) and B's one day work = 1/x
ATQ,
(A+B)'s one day work = 1/4
1/x-6 + 1/x = 1/4
x+x-6 / x(x-6) = 1/4
2x-6 / x(x-6) = 1/4
cross multiplying
8x - 24 = x² - 6x
x² -14x +24 = 0
x² -12x - 2x + 24 = 0
x(x-12) - 2(x-12) = 0
(x-12)(x-2) = 0
x = 12 or 2
x≠2, ∵if x = 2, then A alone can finish work in = (2 - 6) = -4 days, which is not possible.
∴, x = 12, i.e B alone can finish work in 12 days and A alone will finish the work in (12 - 6) = 6 days.
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