An article of cost price Rs. 8000 is marked at Rs. 11200, after allowing a discount of x percent a profit of 12% is made. The value of x is = ?

Solution (By Examveda Team)

Cost price of the article = Rs. 8000
Profit% = 12%
Selling price of the article
$$\eqalign{ & {\text{ = Cost price}} \times \frac{{100 + {\text{P}}\% }}{{100}}{\text{ }} \cr & = 8000 \times \frac{{112}}{{100}} \cr & {\text{ = Rs}}{\text{. 8960}} \cr} $$
$$\eqalign{ & \therefore {\text{ Discount }} \cr & {\text{ = Marked price}} - {\text{Selling price}} \cr & {\text{ = 11200}} - {\text{8960 }} \cr & {\text{ = Rs}}{\text{. 2240}} \cr} $$
Let the discount percentage = x%
$$\eqalign{ & \therefore \frac{{11200 \times x}}{{100}} = 2240 \cr & \Rightarrow x = \frac{{2240 \times 100}}{{11200}} \cr & \Rightarrow x = 20\% \cr} $$

Alternate :
$$\eqalign{ & \frac{{100 - {\text{D}}\% }}{{100 + {\text{P}}\% }} = \frac{{{\text{Cost price}}}}{{{\text{Marked price}}}} \cr & \Rightarrow \frac{{100 - x}}{{100 + 12}} = \frac{5}{7} \cr & \Rightarrow \frac{{100 - x}}{{112}} = \frac{5}{7} \cr & \Rightarrow 700 - 7x = 560 \cr & \Rightarrow 7x = 700 - 560 \cr & \Rightarrow x = \frac{{140}}{7} \cr & \Rightarrow x = 20\% \cr} $$