The ratio of the amount of work done by (x - 1) labours in (x + 1) days and (x + 1) labours in (x + 2) days is 5 : 6. Then the value of x is ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{From }}{{\text{M}}_1}{{\text{D}}_1} = {{\text{M}}_2}{{\text{D}}_2} \cr & \Rightarrow \frac{{{{\text{M}}_1}{{\text{D}}_1}}}{{{{\text{M}}_2}{{\text{D}}_2}}} = \frac{5}{6} \cr & \Rightarrow \frac{{\left( {x - 1} \right)\left( {x + 1} \right)}}{{\left( {x + 1} \right)\left( {x + 2} \right)}} = \frac{5}{6} \cr & \Rightarrow \frac{{\left( {x - 1} \right)}}{{\left( {x + 2} \right)}} = \frac{5}{6} \cr & \Rightarrow 6x - 6 = 5x + 10 \cr & \Rightarrow x = 16 \cr} $$