Question

If the work done by $x-1$ men in $x+1$ days is to the work done by $x+2$ men in $x-1$ days in the ratio of $9:10$, find $x$.

Answer 1

Work done will be directly proportional to number of men and days.

So according to the question,

$\frac{(x-1)(x+1)}{(x+2)(x-1)}=\frac{9}{10}$

Here $x\ne 1$ or else we will get $0$ man and $0$ days and undefined fraction.

$\frac{x+1}{x+2}=\frac{9}{10}$

$10x+10=9x+18$

$x=8$