A radio is sold for Rs. 990 at a profit of 10% . What would have been the actual profit or loss on it had it been sold for Rs. 890 ?

Answer: Option A

Selling price of a radio (SP) = Rs 990
profit (g) = 10%
Let the cost price = CP
$$\begin{array}{rl}& \text{CP}=\frac{\text{SP}\times 100}{100+\text{g}}\\ & \Rightarrow CP=\frac{990\times 100}{100+10}\\ & =\frac{990\times 100}{110}\\ & =\text{Rs}\text{.}900\\ & \text{Now,}\\ & \text{CP}=Rs.900\\ & \text{SP}=Rs.890\\ & \text{CP}>\text{SP}\\ & \text{He}\text{gets}\text{loss}\\ & =\text{Rs}\text{.}900-\text{Rs}\text{.}890\\ & =\text{Rs}\text{.}10\end{array}$$