Question

A takes 6 days less than B to do a 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

Suppose B alone can finish the work in x days.

So, A alone can finish the work in (x − 6) days.

It is given that A and B together can finish the work in 4 days.

∴ Work finished by A and B working together in 1 day = ${\displaystyle \frac{1}{4}}$ .....(1)

Now,

Work finished by B in 1 day = ${\displaystyle \frac{1}{x}}$

Work finished by A in 1 day = ${\displaystyle \frac{1}{x-6}}$

∴ Work finished by A in 1 day work + Work finished by B in 1 day = ${\displaystyle \frac{1}{x-6}+\frac{1}{x}}$ .....(2)

From 1 and 2 we have

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

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

${\displaystyle \Rightarrow \frac{2x-6}{x^2-6x}=\frac{1}{4}}$

⇒ 8x − 24 = x2 − 6x

⇒ x² − 14x + 24 = 0

⇒ x² − 12x − 2x + 24 = 0

⇒ (x − 12)(x − 2) = 0

⇒ x − 12 = 0 or x − 2 = 0

⇒ x = 12 or x = 2

But x cannot be less than 6 because when x is less than 6, then the time taken by A to complete the work is negative, which is not possible.

Therefore, x = 12.

Thus, B alone can finish the work in 12 days