Profit, Loss and Discount made clear.
Use cost price as the base for profit or loss, and marked price as the base for discount. Most errors here come from selecting the wrong denominator.
Key concepts in Profit, Loss and Discount
Profit or loss
Profit = SP−CP; loss = CP−SP. Percentage = difference/CP × 100.
Selling price
At p% profit, SP = CP(1+p/100). At l% loss, SP = CP(1−l/100).
Discount
SP = marked price × (1−discount/100), before any separately stated tax.
Successive changes
Multiply price factors. Two 10% discounts give factor 0.9 × 0.9 = 0.81, or 19% off.
Keep the price bases separate
| Label | What it means | Percentage base |
|---|---|---|
| CP | Cost to seller | Profit and loss |
| MP | Displayed marked price | Discount |
| SP | Actual selling price | Compare with CP to find profit |
A reliable solving method
- Label CP, SP and marked price separately.
- Identify the base used by each percentage.
- Apply successive changes in order with multipliers.
- Check whether the final SP exceeds or falls below CP.
Step-by-step solved examples
An item costs ₹800 and sells for ₹1,000. Find profit %.
- Profit = 1000−800 = ₹200.
- Profit percentage = 200/800 × 100.
- Profit = 25%, not 20%; ₹1,000 is not the base.
A ₹1,500 marked item is discounted by 20%.
- The customer pays 80% of marked price.
- SP = 1500 × 0.8 = ₹1,200.
- Discount amount = ₹300. Profit cannot be found without CP.
An item sells for ₹900 at a 10% loss. Find CP.
- ₹900 represents 90% of CP.
- CP = 900/0.9 = ₹1,000.
- Check: loss ₹100 is 10% of ₹1,000.
Profit, Loss and Discount: practice questions
Choose one answer before opening the explanation. Write down your reasoning as well as the option; a correct guess is different from a method you can repeat.
CP ₹500, SP ₹600: profit %?
Show answer and explanation — question 1
Answer C: 20%
100/500 × 100 = 20%.
Marked ₹800, discount 25%: SP?
Show answer and explanation — question 2
Answer C: ₹600
800 × 0.75 = ₹600.
SP ₹1,200 at 20% profit: CP?
Show answer and explanation — question 3
Answer B: ₹1,000
1200/1.2 = ₹1,000.
Two successive 10% discounts equal?
Show answer and explanation — question 4
Answer C: 19%
1−0.9² = 0.19.
CP ₹400, loss 15%: SP?
Show answer and explanation — question 5
Answer A: ₹340
400 × 0.85 = ₹340.
Which is the base for discount percentage?
Show answer and explanation — question 6
Answer D: Marked price
Discount is measured against marked price.
Frequently asked questions
Can a discounted item still make profit?
Yes. The marked price may be sufficiently above cost price.
How do I recover CP from a profit percentage?
Divide SP by 1 + profit rate as a decimal. Do not subtract that percentage of SP.
Label CP, SP and marked price separately. Check whether the final SP exceeds or falls below CP.