Question

A takes 6 days less than the time taken by B to finish a piece of work. Both A and B together can finish it in 4 days. The time taken by B to finish the work is ___ days.

• A. 12
• B. 14
• C. 10
• D. 8

Answer 1

The correct option is A

12

Suppose B alone can takes $x$ days to finish the work

Then, A alone can finish it in $x-6$ days

B's 1 day's work = $\frac{1}{x}$

A's 1 day's work = $\frac{1}{x-6}$

Given that A and B together finish the work in 4 days, so

(A+B)'s 1 day's work = $\frac{1}{4}$

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

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

$\Rightarrow 8x-24=x^2-6x$

$\Rightarrow x^2-14x+24=0$

$\Rightarrow x^2-12x-2x+24=0$

$\Rightarrow (x-12)(x-2)=0$

$\Rightarrow x=12orx=2$

But $x$ cannot be less than 6

$\Rightarrow x=12$

Hence, B alone can finish the work in 12 days.
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