Understanding the Profit Calculation

This question involves calculating the number of units a business needs to sell to achieve a specific profit target. We are given the sale price per unit, the variable cost per unit, and the total fixed costs.

Key Information Provided

• Sale Price per Unit (SP) = Rs. 50
• Variable Cost per Unit (VC) = Rs. 30
• Fixed Costs (FC) = Rs. 20000
• Target Profit (P) = Rs. 5000

Calculating Contribution Margin

First, we need to determine the Contribution Margin per Unit. This is the amount each unit sold contributes towards covering fixed costs and generating profit. It is calculated as:

$Contribution Margin per Unit = Sale Price per Unit - Variable Cost per Unit$

Using the given values:

$CM = SP - VC$

$CM = \text{Rs. } 50 - \text{Rs. } 30$

$CM = \text{Rs. } 20 \text{ per unit}$

Determining Units for Target Profit

The basic formula for profit is:

$Profit = (Contribution Margin per Unit \times \text{Number of Units Sold}) - Fixed Costs$

In mathematical terms:

$P = (CM \times Q) - FC$

Where:

• $P$ is the Target Profit
• $CM$ is the Contribution Margin per Unit
• $Q$ is the Number of Units to be Sold
• $FC$ is the Fixed Costs

We need to find $Q$. Let's rearrange the formula to solve for $Q$:

$P + FC = CM \times Q$

$Q = \frac{P + FC}{CM}$

Applying the Values

Now, substitute the given values into the rearranged formula:

$Q = \frac{\text{Rs. } 5000 + \text{Rs. } 20000}{\text{Rs. } 20}$

$Q = \frac{\text{Rs. } 25000}{\text{Rs. } 20}$

$Q = 1250 \text{ units}$

Conclusion

Therefore, 1250 units of the product must be sold to achieve a profit of Rs. 5000.