A shopkeeper sells an item for $80 at a profit of 25%. What was the cost price o

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Question: A shopkeeper sells an item for $80 at a profit of 25%. What was the cost price of the item?

Options:

Correct Answer: $60

Solution:

Let the cost price be x. Selling Price = x + 25% of x = 1.25x. Therefore, 1.25x = 80. x = 80 / 1.25 = $64.

A shopkeeper sells an item for $80 at a profit of 25%. What was the cost price of the item?

A shopkeeper sells an item for $80 at a profit of 25%. What was the cost price of the item?

Step 1: Understand that the selling price (SP) of the item is $80.
Step 2: Know that the profit is 25% of the cost price (CP).
Step 3: Let the cost price be represented as 'x'.
Step 4: Calculate the selling price using the formula: Selling Price = Cost Price + Profit.
Step 5: Since profit is 25% of the cost price, we can write it as: Profit = 0.25 * x.
Step 6: Substitute the profit into the selling price formula: SP = x + 0.25x.
Step 7: Combine the terms: SP = 1.25x.
Step 8: Set the selling price equal to $80: 1.25x = 80.
Step 9: To find 'x', divide both sides by 1.25: x = 80 / 1.25.
Step 10: Calculate the value: x = 64.
Step 11: Conclude that the cost price of the item is $64.

Profit Calculation – Understanding how to calculate profit based on selling price and cost price.
Percentage Application – Applying percentage increases to determine the selling price from the cost price.
Algebraic Manipulation – Using algebra to solve for the unknown variable (cost price) in an equation.