Profit, Loss, and Discount Calculations
CSEC Mathematics: Consumer Arithmetic
Essential Understanding: Business transactions rely on understanding the relationship between the cost to buy an item, the price it is sold for, and the adjustments made to attract customers. Mastering the difference between Marked Price, Discount, and Profit is crucial for solving real-world financial problems.
Core Concepts
Cost Price (CP)
Definition: The price at which an article is purchased by the seller (including overhead expenses).
Key Point: This is the baseline for calculating profit or loss percentage.
Selling Price (SP)
Definition: The price at which an article is sold to the customer.
Relation: \[ \text{SP} = \text{MP} – \text{Discount} \]
If SP > CP, it’s a Profit. If CP > SP, it’s a Loss.
Discount
Definition: A reduction given on the Marked Price (MP).
Formula: \[ \text{Discount \%} = \left( \frac{\text{Discount}}{\text{MP}} \right) \times 100 \]
Note: Discount is always calculated on the Marked Price, not the Cost Price.
Profit & Loss
Profit: \[ \text{Profit} = \text{SP} – \text{CP} \]
Loss: \[ \text{Loss} = \text{CP} – \text{SP} \]
Percentages: Always calculated using the Cost Price (CP) as the base.
Essential Formulas
Memorize these relationships for the exam:
Interactive Shop Simulator
The Pricing Strategy Lab
Objective: Act as a shop owner. Set your Cost Price and Markup to determine the Marked Price. Then offer a Discount to see how it affects your final Profit.
Worked Example: Successive Percentage Change
A common CSEC question involves applying a markup first, and then a discount. You must find the final profit percentage.
Markup = 25% of \$80 = 0.25 \times 80 = \$20.
MP = CP + Markup = 80 + 20 = \$100.
Discount is 10% of MP.
Discount = 0.10 \times 100 = \$10.
SP = MP – Discount = 100 – 10 = \$90.
Profit = SP – CP = 90 – 80 = \$10.
\[ \% \text{Profit} = \left( \frac{10}{80} \right) \times 100 = 12.5\% \]
Note: The profit is NOT (25% – 10% = 15%). The base for the discount changed!
Key Examination Insights
Common Mistakes
- Calculating discount percentage based on Cost Price instead of Marked Price.
- Calculating profit percentage based on Selling Price. (Always use Cost Price as the denominator).
- Assuming that Markup % and Profit % are the same (they are only the same if there is no discount).
Success Strategies
- The “$100” Method: If stuck on percentages, assume the Cost Price is \$100. It makes finding values like 20% much easier (\$20).
- Reverse Percentages: If an item is sold for \$90 at a 10% loss, the calculation is \( 90 \div 0.90 = 100 \). Do not calculate 10% of 90 and add it.
CSEC Practice Arena
Test Your Understanding
\[ \% \text{Profit} = \left( \frac{5,000}{20,000} \right) \times 100 = \frac{1}{4} \times 100 = 25\% \]
Selling Price = Marked Price – Discount = \(40 – 6 = \$34\).
\[ SP = 0.90 \times CP \]
\[ 810 = 0.90 \times CP \]
\[ CP = \frac{810}{0.90} = \$900 \]
CSEC Examination Mastery Tip
Watch the Base! (The “OF” word): Whenever you see “OF”, that number is the denominator (the base).
- Profit OF Cost Price \(\rightarrow\) divide by Cost Price.
- Discount OF Marked Price \(\rightarrow\) divide by Marked Price.
- Sales Tax OF Selling Price \(\rightarrow\) divide by Selling Price.