A person sold an article at a loss of $8\%$. Had he sold it at a gain of $10.5\%$, he would have received $\text{Rs. }74$ more. What is the cost price (in $\text{Rs.}$) of the article?

Let the cost price ($CP$) of the article be $100\%$.Initial Selling Price ($S{P}_1$) at an $8\%$ loss = $100\%-8\%=92\%$ New Selling Price ($S{P}_2$) at a $10.5\%$ gain = $100\%+10.5\%=110.5\%$ The difference between the two selling prices is given as $\text{Rs. }74$:
$$110.5\%-92\%=74$$
$$18.5\%=74$$
Now, calculate $100\%$ ($CP$):
$$1\%=\frac{74}{18.5}=4$$
$$100\%=4\times 100=400$$
Thus, the cost price of the article is $\text{Rs. }400$.