A watch is sold at a profit of 20%. If both the cost price and the selling price of the watch are decreased by Rs. 100, the profit would be 5% more. Original cost price of the watch is -

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let C}}{\text{.P}}{\text{. be Rs}}{\text{. }}x \cr & {\text{Profit}} = 20\% \cr & {\text{S}}{\text{.P}}{\text{.}} = 120\% {\text{ of Rs}}{\text{. }}x \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\frac{{6x}}{5} \cr & {\text{New C}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {x - 100} \right) \cr & {\text{New S}}{\text{.P}}{\text{.}} = {\text{Rs}}.\left( {\frac{{6x}}{5} - 100} \right) \cr} $$
$$\eqalign{ & {\text{Profit = }} \cr & {\text{Rs}}.\left[ {\left( {\frac{{6x}}{5} - 100} \right) - \left( {x - 100} \right)} \right] \cr & = {\text{Rs}}.\frac{x}{5} \cr & \therefore \frac{x}{5} \times \frac{1}{{\left( {x - 100} \right)}} \times 100 = 25 \cr & \Rightarrow 20x = 25\left( {x - 100} \right) \cr & \Rightarrow 5x = 2500 \cr & \Rightarrow x = 500 \cr} $$