Question

Two workers $A$ and $B$ are engaged to do a piece of work. Working alone, $A$ takes $8$ hours more to complete the work than if both worked together. On the other hand, working alone, $B$ would need $4\frac{1}{2}$ hours more to complete the work than if both worked together. How much time would they take to complete the job working together?

• A. $4$ hours
• B. $5$ hours
• C. $6$ hours
• D. $7$ hours

Answer 1

Answer: (C)

$6$ hours

Let the number of hours taken by A and B both to complete the work be $x$.

As per the given information, A takes $x+8$ hours to complete when he works alone.

Similarly, B takes $x+4.5$ hours to complete the work, working alone.

$\therefore \frac{1}{x+4.5}+\frac{1}{x+8}=\frac{1}{x}$

$\Rightarrow (x+8+x+4.5)x=(x+4.5)(x+8)$

$\Rightarrow 2x^2+12.5x=x^2+12.5x+36$

$\Rightarrow x^2=36$ or $x=6$ hours