A trader carries an average inventory of Rs. 40,000. His inventory turnover ratio is 8 times. If he sells goods ata profit of 20% on Revenue from operations, find out the gross profit.

The correct option is Rs. 80,000.

Let us break down the solution step-by-step to understand how we arrive at this answer.

Step 1: Understand the given information
We are given the following values:
1. Average Inventory = Rs. 40,000
2. Inventory Turnover Ratio = 8 times
3. Gross Profit Rate = 20% on Revenue from operations (Net Sales)

Step 2: Calculate the Cost of Revenue from Operations (Cost of Goods Sold)
The formula for the Inventory Turnover Ratio is:

$$\text{Inventory Turnover Ratio}=\frac{\text{Cost of Revenue from Operations}}{\text{Average Inventory}}$$
Substituting the given values into the formula:

$$8=\frac{\text{Cost of Revenue from Operations}}{\mathrm{40,000}}$$
Now, solving for the Cost of Revenue from Operations:

$$\text{Cost of Revenue from Operations}=8\times \mathrm{40,000}=\text{Rs. 3,20,000}$$

Step 3: Establish the relationship between Revenue, Cost, and Gross Profit
Let the Revenue from operations (Net Sales) be S.
The Gross Profit is given as 20% of the Revenue from operations.
Therefore:

$$\text{Gross Profit}=0.20\times S$$
We also know the fundamental accounting equation:

$$\text{Cost of Revenue from Operations}=\text{Revenue from Operations}-\text{Gross Profit}$$
Substituting our terms into this equation:

$$\mathrm{3,20,000}=S-0.20S$$
Simplify the right side of the equation:

$$\mathrm{3,20,000}=0.80S$$
Now, solve for the Revenue from operations (S):

$$S=\frac{\mathrm{3,20,000}}{0.80}=\text{Rs. 4,00,000}$$

Step 4: Calculate the Gross Profit
Now that we have the Revenue from operations (Rs. 4,00,000), we can find the Gross Profit:

$$\text{Gross Profit}=20\%\text{of Rs. 4,00,000}$$
$$\text{Gross Profit}=\frac{20}{100}\times \mathrm{4,00,000}=\text{Rs. 80,000}$$
Thus, the gross profit is indeed Rs. 80,000.