The cost price of 80 articles is ? 12.50 per article. Twenty...

The cost price of 80 articles is $? 12.50$ per article. Twenty of them were sold for $? 18$ each. At what price should each of the remaining articles be sold so as to get an overall profit of $? 4.50$ per article?
(A) $? 15$
(B) $? 16 \frac{2}{3}$
(C) $? 17 \frac{1}{3}$
(D) $? 18$

Key Concepts

Cost Price

This is the amount paid to acquire each unit of an item. In problems like this, the total cost is calculated by multiplying the unit cost by the total number of items. Understanding cost price is fundamental for determining profitability and setting sales targets.

Selling Price

This refers to the price at which an item is sold. It determines the revenue per unit and, when compared with the cost price, helps in calculating the profit or loss made per unit. Adjusting the selling price is often necessary to meet overall profit targets.

Profit

Profit is the financial gain obtained when the selling price exceeds the cost price. In problems involving multiple items, profit can be calculated per item or in total, and it plays a crucial role in decision-making regarding pricing strategies.

Overall Profit Target

This concept involves setting a desired profit amount per unit or in total for all items sold. It requires balancing different selling prices across different batches of items to achieve the targeted profit, often through weighted averages and equations.

Equation Formulation

This involves setting up an algebraic equation that represents the relationship between total cost, total revenue, and desired overall profit. It is a systematic method of linking known values to unknown variables, such as the required selling price for remaining items, ensuring that the final solution meets the profit objectives.

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