An article is sold at 25 percent loss. If its cost price is doubled and selling price is increased by Rs. 660, then there is a profit of 20 percent. What is the original cost price of the article?

Solution (By Examveda Team)

$$\eqalign{ & {\bf{Given:}} \cr & \frac{{{\text{CP}} - {\text{SP}}}}{{{\text{CP}}}} \times 100 = 25 - - - \left( 1 \right) \cr & \frac{{{\text{SP}} + 660 - 2{\text{CP}}}}{{2{\text{CP}}}} \times 100 = 20 - - - \left( 2 \right) \cr & {\bf{Formula}}\,{\bf{used:}} \cr & {\text{Profit }}\% = \frac{{{\text{Profit}}}}{{{\text{CP}}}} \times 100 \cr & {\text{Loss }}\% = \frac{{{\text{Loss}}}}{{{\text{CP}}}} \times 100 \cr & {\text{Profit}} = {\text{SP}} - {\text{CP}} \cr & {\text{Loss}} = {\text{CP}} - {\text{SP}} \cr & {\text{CP}} = {\text{Cost price}} \cr & {\text{SP}} = {\text{Selling price}} \cr & {\bf{Solution:}} \cr & {\text{Let's solve the first equation,}} \cr & 1 - \frac{{{\text{SP}}}}{{{\text{CP}}}} = 0.25 \cr & \frac{{{\text{SP}}}}{{{\text{CP}}}} = 0.75 \cr & {\text{SP}} = 0.75{\text{CP}} \cr & {\text{Now, let's put the value of SP in the second equation,}} \cr & \frac{{0.75{\text{CP}} + 660 - 2{\text{CP}}}}{{2{\text{CP}}}} \times 100 = 20 \cr & \frac{{660 - 1.25{\text{CP}}}}{{2{\text{CP}}}} = 0.2 \cr & 660 - 1.25{\text{CP}} = 0.4{\text{CP}} \cr & {\text{CP}} = \frac{{660}}{{1.65}} \cr & {\text{CP}} = 400 \cr & {\text{The original cost price is Rs}}{\text{. 400}} \cr} $$