Please help me in solving this question....

Dear Student,
Solution)Let marked price  =  Rs . 100 
Given discount is 20%  , So
Selling price =  100 - 20% of 100
                       =  100 - $\frac{20 \times 100}{100}$ 
                       = 100 - 20 
                       = Rs. 80

And trader gets 10% profit by selling at Rs 80 .

Let Cost price  =  x  
So,  x  +  10% of x  =  80
$$\begin{gathered} \Rightarrow x + \frac{10x}{100} = 80 \\ \Rightarrow x + \frac{x}{10} = 80 \\ \Rightarrow \frac{11x}{10} = 80 \\ \mathbf{\Rightarrow }\mathit{x}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{ }\mathbf{800}}{\mathbf{11}} \end{gathered}$$

And new discount is 10% 

New selling price  =  100 - 10% of 100
                                 = 100 - $\frac{10 \times 100}{100}$ 
​​​​                                  = 100 - 10 
                                  = Rs .90

So, New Profit = 90 - $\frac{800}{11} = \frac{990 - 800}{11} = \frac{\mathbf{190}}{\mathbf{11}}$

Then ,

Profit % = $\frac{{\displaystyle \frac{190}{11}}}{{\displaystyle \frac{800}{11}}} \times 100 = \frac{190}{11}\times \frac{11}{800}\times 100 = \frac{190}{8} = \frac{95}{4} = \mathbf{23}\frac{\mathbf{3}}{\mathbf{4}}\mathbf{\%}$

Option ( D )  is correct.                                       

Regards!