Calculating Profit, Selling Price, and Discount on Handbags
To solve this question, we first need to calculate the cost price of the handbags, then determine the selling price that would result in a 24% profit, and finally apply the discount to find out the price that should be marked on the label.
The cost price (CP) is given as R172.00.
Next, we calculate the selling price (SP) for a 24% profit.
Profit is calculated by the formula: Profit = SP - CP
We know the Profit should be 24% of CP. So, the equation for profit becomes:
0.24 * CP = SP - CP
Now, let's insert the value of CP (R172.00) into this equation:
0.24 * 172 = SP - 172
Solving for SP gives us:
41.28 = SP - 172
SP = 172 + 41.28
SP = 213.28
This is the price before discount at which the merchant should sell the handbags to gain a 24% profit. However, the merchant wants to offer a 14% discount on this selling price.
Discount is calculated by the formula: Discounted Price = Original Price - (Discount Percentage * Original Price)
Let's apply the 14% discount to the SP of R213.28:
Discounted Price = 213.28 - (0.14 * 213.28)
Calculating the discount amount gives us:
Discount Amount = 0.14 * 213.28
Discount Amount = 29.8592
Now we can determine the discounted price to be marked on the label:
Discounted Price = 213.28 - 29.8592
Discounted Price = 183.4208
Since the listed choices are rounded to two decimal places, the price that should be marked on the label is R183.42.
Hence, the correct answer is:
a. R183.42
