Question

A certain number of men can finish a piece of work in 100 days. If how ever, there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally ? [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 3 Marks

Let numbers of men = x

$\begin{array}{ccc}No.ofmen& x& x-10\\ No.ofdays& 100& 110\end{array}$

Now number of men is inversely proportional to the no. of of days

$\therefore x\times 100=(x-10)110$

$x\times 100=(x-10)110$

$\Rightarrow 100x=(x-10)110$

$=110x-1100$

$\Rightarrow 1100=110x-100x$

$\therefore 1100=10x$

​$x=110$

Hence, there were 110 men originally.