Question

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, find the time taken by B alone to finish the work.

• A. B alone can finish the work in 9 days
• B. B alone can finish the work in 8 days
• C. B alone can finish the work in 12 days
• D. B alone can finish the work in 5 days

Answer 1

The correct option is C

B alone can finish the work in 12 days

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 = $\frac{1}{x-6}$.
(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