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's find the marked price per unit step-by-step.

Let the fixed marked price of the product per unit be $M$ rupees.

Step 1: Calculate the selling price (SP) per unit for each month
Based on the given discounts, we can express the selling price for each month in terms of $M$:
- January: A discount of 20% is given on the marked price.

${\text{SP}}_{\text{January}}=M\times (1-0.20)=0.80M$

- February: A discount of 10% is given on the marked price.

${\text{SP}}_{\text{February}}=M\times (1-0.10)=0.90M$

- March: A discount of 5% is given on the marked price.

${\text{SP}}_{\text{March}}=M\times (1-0.05)=0.95M$

- April: No discount is given on the marked price.

${\text{SP}}_{\text{April}}=M$

Step 2: Calculate the total revenue generated from sales
Multiply the sales volume of each month by its respective selling price per unit:
- January sales: 120 units

${\text{Revenue}}_{\text{January}}=120\times 0.80M=96M$

- February sales: 135 units

${\text{Revenue}}_{\text{February}}=135\times 0.90M=121.5M$

- March sales: 150 units

${\text{Revenue}}_{\text{March}}=150\times 0.95M=142.5M$

- April sales: 165 units

${\text{Revenue}}_{\text{April}}=165\times M=165M$

Summing these up to find the total revenue:

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

Step 3: Calculate the total cost price (CP)
First, find the total number of units sold from January to April:

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

Given that the cost price of the product was Rs. 240 per unit, the total cost price is:

$\text{Total CP}=570\times 240=136800\text{rupees}$

Step 4: Use the total profit to solve for the marked price ($M$)
We know that:

$\text{Total Profit}=\text{Total Revenue}-\text{Total CP}$

Given that the total profit was Rs. 138825, we set up the equation:

$525M-136800=138825$

Add 136,800 to both sides of the equation:

$525M=138825+136800$

$525M=275625$

Solve for $M$ by dividing both sides by 525:

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

$M=525$

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