To calculate the percentage margin on a product, we start by defining the terms involved in the problem:
- Cost: The amount it takes to produce or purchase the product.
- Price: The amount at which the product is sold to customers.
- Margin: The difference between the selling price and the cost.
The margin can also be calculated as a percentage, which is called the percentage margin. This is determined by dividing the margin by the price and then converting it to a percentage.
Given that the price is set at 3 times the cost, we represent the cost as 'C' and the price as 'P'. Thus:
P = 3C
Now we want to find the margin:
Margin = P - C
Margin = 3C - C
Now, we simplify the margin equation:
Margin = 3C - C
Margin = 2C
To find the percentage margin, we divide the margin by the price and then multiply by 100 to convert it to a percentage:
Percentage Margin = (Margin / P) 100
Substitute Margin and P in the above formula:
Percentage Margin = ((2C) / (3C)) 100
Cancelling out 'C' from the numerator and denominator (since it's a common factor and not equal to zero), we get:
Percentage Margin = (2 / 3) 100
Now we calculate the numerical value:
Percentage Margin = 0.6666... 100
When converted to a percentage, this is:
Percentage Margin = 66.6666...%
In terms of percentage points, this is commonly rounded to the nearest whole number, so:
Percentage Margin ≈ 67%
Therefore, the correct answer to the question is:
b) 67%
