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Numerical Questions · Q15

Q.A trading firm's average inventory is ₹20,000 (cost). If the inventory turnover ratio is 8 times and the firm sells goods at a gross profit of 20% on sales, ascertain the gross profit of the firm.

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The firm's gross profit is ₹40,000, derived from the inventory turnover ratio and the given gross profit margin on sales.

Concept First: What the Inventory Turnover Ratio Tells Us

The inventory turnover ratio measures how many times a firm sells and replaces its average inventory during a period. The formula is:

Inventory Turnover Ratio = Cost of Revenue from Operations (Cost of Goods Sold) / Average Inventory

Here, the ratio is 8 times, and average inventory is ₹20,000. This directly tells us the cost of goods sold (COGS) — the total cost of inventory that was sold during the year.

Once we know COGS, we can work backwards to find Sales using the gross profit percentage. The key point: gross profit is given as 20% on sales, meaning:

  • If Sales = 100%, then Gross Profit = 20% of Sales, and COGS = 80% of Sales.

So COGS is 80% of Sales. Once we find Sales, we can compute Gross Profit.


Step-by-Step Solution

Step 1: Find Cost of Goods Sold (COGS)

Using the inventory turnover ratio:

Inventory Turnover Ratio = COGS / Average Inventory

Given: Ratio = 8 times, Average Inventory = ₹20,000

So:

8 = COGS / 20,000

COGS = 8 × 20,000 = ₹1,60,000


Step 2: Relate COGS to Sales using Gross Profit Percentage

Gross profit is 20% on sales. This means:

Let Sales = S

Then Gross Profit = 20% of S = 0.20 S

And COGS = Sales – Gross Profit = S – 0.20 S = 0.80 S

We already know COGS = ₹1,60,000

So:

0.80 S = 1,60,000

S = 1,60,000 / 0.80 = ₹2,00,000


Step 3: Compute Gross Profit

Gross Profit = Sales – COGS

= 2,00,000 – 1,60,000 = ₹40,000

Alternatively, directly: Gross Profit = 20% of Sales = 20% of 2,00,000 = ₹40,000


Working Notes

Working NoteCalculationResult
1. COGS8 × 20,000₹1,60,000
2. Sales1,60,000 ÷ 0.80₹2,00,000

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