₹ 1,00,000 is net sales of a concern during 2021. If inventory turnover is 4 times, calculate the inventory at the end is 1.5 times of that is the beginning:

Question

Accepted Answer

The correct option is 2: ₹ 30,000.

The correct option is 2: ₹ 30,000
To find the closing inventory (inventory at the end), we must use the Inventory Turnover Ratio (ITR) formula, which is typically calculated as Cost of Goods Sold (COGS) divided by Average Inventory. Since the Cost of Goods Sold is not given, in the context of this problem, we must assume that the Net Sales amount of ₹ 1,00,000 is used as a proxy for COGS. First, we determine the Average Inventory: ITR = COGS / Average Inventory, so 4 = ₹ 1,00,000 / Average Inventory, yielding an Average Inventory of ₹ 25,000. Next, we use the average inventory formula: Average Inventory = (Opening Inventory + Closing Inventory) / 2. We also know that Closing Inventory is 1.5 times the Opening Inventory. Let Opening Inventory be $X$. Then, ₹ 25,000 = ($X$ + $1.5X$) / 2. Solving this, $50,000 = 2.5X$, which means the Opening Inventory ($X$) is ₹ 20,000. Therefore, the Closing Inventory is $1.5 \times ₹ 20,000$, which correctly gives ₹ 30,000.

The incorrect option is 1: ₹ 20,000
This value represents the Opening Inventory, not the required Closing Inventory. In our calculation, after finding the average inventory of ₹ 25,000, we established that the Opening Inventory ($X$) is ₹ 20,000. The question specifically asks for the inventory at the end (Closing Inventory), which is 1.5 times the beginning inventory. Choosing ₹ 20,000 indicates a conceptual error in identifying the final required value from the calculated figures. Students should always read the final requirement of the question carefully.

The incorrect option is 3: ₹ 13,333
This answer results from incorrectly calculating the average inventory or applying the ratio. If one mistakenly calculated the opening inventory ($X$) by dividing the total of ₹ 50,000 by 3.75 (a derived miscalculation: $1.5+1+1.25$ or similar), this figure could be obtained. Specifically, dividing ₹ 50,000 by 3 gives ₹ 16,666.67, and dividing ₹ 1,00,000 by 7.5 (a misapplication of the ratio of 1.5 and turnover of 4) results in a number close to this. The error lies in the fundamental algebraic setup of the inventory relationship.

The incorrect option is 4: ₹ 10,000
This figure is derived from an incorrect calculation of the Average Inventory. If a student mistakenly calculated the Average Inventory as ₹ 10,000 (perhaps by dividing the Net Sales by 10 instead of 4), then the total of Opening + Closing Inventory would be ₹ 20,000. Using the ratio $2.5X = ₹ 20,000$ would give $X = ₹ 8,000$, and Closing Inventory of $1.5 \times ₹ 8,000 = ₹ 12,000$. Hence, ₹ 10,000 is a figure that results from a severe initial miscalculation, particularly a mistake in the application of the Inventory Turnover Ratio formula or the assumption of the Average Inventory value.