Question

A certain number of men complete a piece of work in 28 days. If there were 10 men more, the work could be finished in 8 days before (less), then how many men were originally there?

Answer 1

 Let there be $x$ men originally.

Now, $x$ men finish the work in 28 days

$\Rightarrow 1$ man can finish it in $28 x$ days Again, $(x+10)$ men finish the work in $(28-8)=20$ days

$\Rightarrow 1$ man finishes the work in

$20(x+10)$ days

From the question,

$$

\begin{aligned}

& 28 x=20(x+10) \\

\Rightarrow & 28 x=20 x+200 \\

\Rightarrow & 28 x-20 x=200 \\

\Rightarrow & 8 x=200 \\

\therefore & x=\frac{200}{8}=25 \text { men; Ans. }

\end{aligned}

$$