If the work done by (x - 1) men in (x + 1) days and the work done by (x + 2) men in (x - 1) days are in the ratio 9 : 10, then the value of x is equal to ?

Put values in formula
$$\frac{{{{\left( {x - 1} \right)}_{{\text{men}}}} \times {{\left( {x + 1} \right)}_{{\text{days}}}}}}{{{{\text{9}}_{{\text{work}}}}}} = $$       $$\frac{{{{\left( {x + 2} \right)}_{{\text{men}}}} \times {{\left( {x - 1} \right)}_{{\text{days}}}}}}{{{{10}_{{\text{work}}}}}}$$
$$\eqalign{ & \Rightarrow \frac{{x + 1}}{9} = \frac{{x + 2}}{{10}} \cr & \Rightarrow 10x + 10 = 9x + 18 \cr & \Rightarrow x = 8 \cr} $$