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 = ?

Answer: Option B

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

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