The monthly sales of a product from January to April were 120, 135, 150 and 165 units, respectively. The cost price of the product was Rs. 240 per unit, and a fixed marked price was used for the product in all the four months. Discounts of 20%, 10% and 5% were given on the marked price per unit in January, February and March, respectively, while no discounts were given in April. If the total profit from January to April was Rs. 138825, then the marked price per unit, in rupees, was

The total number of products is $$120+135+150+165= 570$$. Therefore, the total cost must have been $$570\times 240 = 136800$$

Let the marked price for the products be $$X$$. The January, February, March, and April, selling prices would respectively be $$0.8X$$, $$0.9X$$, $$0.95X$$, and $$X$$; based on the discounts given on each of the months.

The revenue earned from selling the products in each of the months would be: $$120*0.8X + 135*0.9X + 150*0.95X + 165*X = 525X$$.

The profit earned would be: Revenue -  Cost, and therefore, 

$$525X - 136800 = 138825$$

$$525X = 275625$$

$$X = \dfrac{275625}{525} = 525$$

The correct answer is option B, Rs. 525.