The reduction of Rs. 12 in the selling price of an article will changes 5% gain into $${\text{2}}\frac{1}{2}$$% lose. The cost price of the article is = ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{cost}}\,{\text{price}}\,{\text{be}}\,x \cr & {\text{gain}} = 5\% \cr & {\text{Selling}}\,{\text{Price}} = \frac{{105x}}{{100}} \cr & {\text{New}}\,{\text{SP}} = \frac{{105x}}{{100}} - 12 \cr & {\text{Now}}\,{\text{there}}\,{\text{is}}\,{\text{a}}\,{\text{loss}}\,{\text{of}}\,2.5\% \cr & x \times \frac{{100 - 2.5}}{{100}} = \frac{{105x}}{{100}} - 12 \cr & \frac{{97.5x}}{{100}} = \frac{{105x}}{{100}} - 12 \cr & 97.5x = 105x - 1200 \cr & 7.5x = 1200 \cr & \therefore x = 160 \cr} $$