Question

'X' men can complete the last set of work in 40 days. If there were 8 men more, the work could be finished in 10 days less. The original number of men is?​

Answer 1

This is the method for this question

Answer 2

$\begin{gathered}{\underline{\underline{\maltese{\Huge{\textsf{\textbf{\red{Solution: }}}}}}}}\end{gathered}$

$\sf{\bold Let \: there \: be \: x \: men \: originally.}$

x men finish the work in 40 days and (x+8) finish it in 30 days.

$\sf{x \: men \: finish \: the \: job \: in \: 40 \: days.}$

$\sf{1 \: man \: can \: finish \: it \: in \: 40x \: days.}$

$\sf{(x+8) \: men \: can \: finish \: the \: job \: in \: 30 \: days.}$

$\sf{1 \: man \: can \: finish \: it \: in \: 30(x+8) \: days.}$

Therefore,

$\implies\sf{40x=30(x+8)}$

$\implies\sf{40x = 30x + 240}$

$\implies\sf{10x=240}$

$\implies\sf{x=24}$

Hence, there were 24 men originally.