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 correct option is 525.

Let the marked price of the product per unit be Rs. $M$.
The cost price per unit is given as Rs. 240.

Let us analyze the sales, selling price per unit, and total revenue for each of the four months:

1. January:
Units sold = 120
Discount = 20%
Selling price per unit = $M\times (1-0.20)=0.80M$
Revenue in January = $120\times 0.80M=96M$

2. February:
Units sold = 135
Discount = 10%
Selling price per unit = $M\times (1-0.10)=0.90M$
Revenue in February = $135\times 0.90M=121.5M$

3. March:
Units sold = 150
Discount = 5%
Selling price per unit = $M\times (1-0.05)=0.95M$
Revenue in March = $150\times 0.95M=142.5M$

4. April:
Units sold = 165
Discount = 0%
Selling price per unit = $M$
Revenue in April = $165\times M=165M$

Now, let us calculate the total revenue from January to April:

$\text{Total Revenue}=96M+121.5M+142.5M+165M=525M$

Next, let us calculate the total number of units sold and the total cost price:

$\text{Total Units Sold}=120+135+150+165=570\text{units}$

$\text{Total Cost Price}=570\times 240=\text{Rs.}136800$

We are given that the total profit is Rs. 138825.
Using the relation $\text{Total Profit}=\text{Total Revenue}-\text{Total Cost Price}$:

$138825=525M-136800$

$525M=138825+136800$

$525M=275625$

$M=\frac{275625}{525}=525$

Therefore, the marked price per unit was Rs. 525.