Answer: Option A
:
A
Let the marked price of the book be x.
Selling Price (SP) after discount of $30\%$
$=x(1-\frac{30}{100})=\frac{7x}{10}$
It is known that there is a profit of $20\%$ of SP $\frac{7x}{10}$
$\therefore CP=\frac{7x}{10}\left(\frac{100}{100+20}\right)=\frac{7x}{12}.$
New SP=x-400 and on this new SP there is a loss of $20\%$.
$\Rightarrow \frac{7x}{12}(1-\frac{20}{100})=x-400$
$\Rightarrow \frac{7x}{15}=x-400\Rightarrow 400=x-\frac{7x}{15}$
$\Rightarrow \frac{9x}{15}=400\Rightarrow x=750$
Shortcut- Using the reverse Gear Approach
Always start with a middle answer option
Assuming 750 as the right answer option.
If he gives a discount of 30% then the selling price will be 750 - 225=525, with which he is able to make a profit of $20\%$.
Thus, cost price will be $=\left(\frac{525}{1.20}\right)=437.5$
Again if he had given a discount of 400 Rs. He would have sold the book at 750 - 400=350 he incurred a loss of $20\%$ or $\left(\frac{350}{0.8}\right)$=437.5hence that is the correct option.