John sold an article for $105,000.00 at a loss of $4\%. Find the cost price of the article.
A. $N 100,800.00
B. $105,400.00
C. $N 109,200.00
D. $N 109,375.00
Answer (2)
Let C be the cost price.
Express the selling price as 105000 = C − 0.04 C .
Simplify the equation to 105000 = 0.96 C .
Solve for C : C = 0.96 105000 = 109375 .
Explanation
Understanding the Problem Let's analyze the problem. John sold an article at a loss of 4%, and we know the selling price. We need to find the original cost price of the article.
Setting up the Equation Let the cost price of the article be C . The loss is 4% of the cost price, which can be written as 0.04 × C = 0.04 C . The selling price is the cost price minus the loss.
Formulating the Equation We can express the selling price ( S ) as: S = C − 0.04 C . We are given that the selling price is $105 , 000.00 . So, we have the equation: 105000 = C − 0.04 C .
Solving for the Cost Price Now, we simplify the equation: 105000 = C ( 1 − 0.04 ) = 0.96 C . To find the cost price C , we divide both sides of the equation by 0.96 : C = 0.96 105000 .
Calculating the Cost Price Calculating the value of C : C = 0.96 105000 = 109375 . Therefore, the cost price of the article is $109 , 375.00 .
Examples
Understanding cost price and loss percentages is crucial in business. For example, if a store buys a product for a certain cost and needs to set a selling price that accounts for potential losses (due to damage, theft, or spoilage), they need to calculate the selling price to ensure they still make a profit. This involves understanding the relationship between cost price, selling price, and loss percentage. This type of calculation is also important in personal finance when selling items, such as a car or furniture, to ensure you're not selling at too great a loss.
John sold the article for $105,000 at a 4% loss, meaning he sold it for 96% of its cost price. By setting up the equation 105000 = 0.96 C and solving for C , we find that the cost price is 109 , 375.00. T h ere f ore , t h ecorrec t an s w er i so pt i o n D : N 109,375.00.
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