One trader calculates the percentage of profit on the buying price and another calculates on the selling price. When their selling price are the same then the difference of their actual profits is Rs. 85 and both claim to have made 20% profit, what is the selling price of each ?

For the first trader,
Let the CP of the article = Rs. 100
⇒ SP = Rs. 120
Now, For the second trader,
SP of the article = Rs. 120
& Gain = 20%
Let the CP be Rs. x
$$\eqalign{ & \therefore \frac{{120 - x}}{{120}} \times 100 = 20 \cr & \therefore 120 - x = 20 \times \frac{6}{5} = 24 \cr & \therefore x = 120 - 24 = {\text{Rs}}{\text{.}}\,96 \cr & \therefore {\text{Gain}} = {\text{Rs}}{\text{.}}\,24 \cr} $$
Now when difference of gain = Rs. 4
Then SP = Rs. 120
So, When the difference = Rs. 85
Then
$$\eqalign{ & {\text{SP}} = \frac{{120}}{4} \times 85 \cr & \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,2550 \cr} $$