To solve the problem, we need to compute the average amount of stock in hand at cost price based on the information provided. Let's break down the steps systematically.
Step 1: Understand the Selling Price and Cost Price Relationship
The retailer adds one-quarter (25%) to the cost of the article to determine the selling price. This means if the cost price (CP) is represented as ( CP ), the selling price (SP) can be calculated as follows:
[
SP = CP + \frac{1}{4}CP = \frac{5}{4}CP
]
Step 2: Calculate the Cost Price from Total Sales
We know the total sales amount is N23,000. To find the cost price, we first need to determine how much of the sales corresponds to the cost price. Since the selling price is 125% of the cost price, we can express the total sales in terms of cost price:
[
Total\ Sales = \frac{5}{4} \times Total\ Cost\ Price
]
Let ( Total\ Cost\ Price = CP_{total} ). Then we can set up the equation:
[
N23,000 = \frac{5}{4} \times CP_{total}
]
To find ( CP_{total} ), we rearrange the equation:
[
CP_{total} = N23,000 \times \frac{4}{5} = N18,400
]
Step 3: Calculate Average Stock
The retailer turned over his stock five times in the year. The stock turnover ratio is defined as:
[
Stock\ Turnover\ Ratio = \frac{Cost\ of\ Goods\ Sold}{Average\ Stock}
]
From the information given, we can express the cost of goods sold (COGS) as equal to the total cost price since all stock was sold during the year:
[
COGS = CP_{total} = N18,400
]
Using the stock turnover ratio, we can rearrange to find the average stock:
[
Average\ Stock = \frac{COGS}{Stock\ Turnover\ Ratio}
]
Substituting the values we have:
[
Average\ Stock = \frac{N18,400}{5} = N3,680
]
Conclusion: Final Answer
Thus, the average amount of stock in hand at cost price is
N3,680. Therefore, the correct option is
C.
Explanation of Other Options
- Option A: N3,860 - This value is higher than the calculated average stock and does not align with the turnover ratio.
- Option B: N3,806 - This value is also incorrect as it does not match the calculated average stock.
- Option D: N3,086 - This is significantly lower than the calculated average stock and does not reflect the turnover ratio.
Revision Summary
- The selling price is calculated as 125% of the cost price.
- Total sales of N23,000 correspond to a total cost price of N18,400.
- The average stock is calculated using the stock turnover ratio, which is derived from the total cost price divided by the number of turnovers.
- The average stock in hand at cost price is N3,680, corresponding to option C.