Ramesh sold a book at a loss of 30%. If he has sold it for Rs. 140 more, he would have made a profit of 40%. The cost price of the book is = ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Loss}} = 30\% \cr & {\text{Let}}\,{\text{CP}} = x \cr & {\text{Loss}}\% = \frac{{{\text{CP}} - {\text{SP}}}}{{{\text{CP}}}} \times 100 \cr & \Rightarrow \frac{{30}}{{100}} = \frac{{x - {\text{SP}}}}{x} \cr & \Rightarrow 3x = 10x - 10{\text{SP}} \cr & \Rightarrow 7x = 10{\text{SP}} \cr & \Rightarrow {\text{SP}} = \frac{7}{{10}}x \cr & {\text{If}}\,{\text{SP}} = 140\,{\text{more}}\, = \frac{7}{{10}}x + 140 \cr & {\text{the}}\,{\text{profit}} = 40\% \cr & \Rightarrow \frac{{40}}{{100}} = \frac{{\frac{7}{{10}}x + 140 - x}}{x} \cr & \Rightarrow \frac{2}{5} = \frac{{1400 - 3x}}{{10x}} \cr & \Rightarrow 4x = 1400 - 3x \cr & \Rightarrow 7x = 1400 \cr & \Rightarrow x = 200 \cr & {\text{So,}}\,{\text{CP}} = {\text{Rs}}{\text{.}}\,200 \cr} $$