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 then if both worked together. On the other hand, working alone, B would need $4\frac{1}{2}$ hours more to complete the work then 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

The correct option is C 6 hours

Let $A$ works at the rate of $a$ units/hr and $B$ works at the rate of $b$ units/hr. $A$and $B$ complete the job in $x$ hrs.

A working alone takes 8 hours more to complete the job than if both worked together.

$\Rightarrow a(x+8)=(a+b)x$

$\Rightarrow ax+8a=ax+bx$

$\Rightarrow 8a=bx$ or $a=\frac{bx}{8}$ ---$\left(1\right)$

If $B$ worked alone, he would need $4.5$ hours more to complete the job than they both working together

$\Rightarrow b(x+4.5)=(a+b)x$

$\Rightarrow bx+4.5b=ax+bx$

$\Rightarrow 4.5b=ax$ or $a=\frac{4.5b}{x}$ ---$\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$, we have

$\frac{bx}{8}=\frac{4.5b}{x}$

$\Rightarrow x^2=4.5\times 8$

$\Rightarrow x^2=36$

$\Rightarrow x=6$

They take $6$hrs to do the work together