Profit and Loss formulas are easy to memorise when you understand which value acts as the base. In ordinary profit and loss questions, Cost Price (CP) is the base. In discount questions, Marked Price (MP) is the base. This formula guide keeps those relationships together so that you can choose the correct expression quickly in SSC, Banking and Railway exams.
1. Core Profit and Loss Formulas
- Profit = SP − CP
- Loss = CP − SP
- Profit% = Profit ÷ CP × 100
- Loss% = Loss ÷ CP × 100
These four formulas are the foundation. The most common mistake is using SP as the denominator for ordinary profit% or loss%.
2. Find SP When CP and Profit% Are Given
If profit is p%, then:
SP = CP × (100 + p) ÷ 100
Example: CP = ₹800 and profit = 25%.
SP = 800 × 125 ÷ 100 = ₹1,000.
3. Find SP When CP and Loss% Are Given
If loss is p%, then:
SP = CP × (100 − p) ÷ 100
Example: CP = ₹800 and loss = 15%.
SP = 800 × 85 ÷ 100 = ₹680.
4. Find CP When SP and Profit% Are Given
If an item is sold at p% profit, the final SP represents (100 + p)% of CP.
CP = SP × 100 ÷ (100 + p)
Example: SP = ₹720 at 20% profit.
CP = 720 × 100 ÷ 120 = ₹600.
5. Find CP When SP and Loss% Are Given
If an item is sold at p% loss, SP represents (100 − p)% of CP.
CP = SP × 100 ÷ (100 − p)
Example: SP = ₹680 at 15% loss.
CP = 680 × 100 ÷ 85 = ₹800.
6. Discount and Discount Percentage Formulas
- Discount = MP − SP
- Discount% = Discount ÷ MP × 100
- SP after p% discount = MP × (100 − p) ÷ 100
- MP when SP and discount% are known = SP × 100 ÷ (100 − p)
Example: MP = ₹1,000 and SP = ₹850. Discount = ₹150 and Discount% = 150 ÷ 1,000 × 100 = 15%.
For deeper MP-SP combinations, use Discount and Marked Price Questions.
7. Successive Discount Formula
For two successive discounts of a% and b%, the effective discount is:
Effective Discount% = a + b − ab/100
Example: 10% and 20% successive discounts:
10 + 20 − (10 × 20)/100 = 28%.
The multiplier method gives the same result: 0.90 × 0.80 = 0.72, so the final price is 72% of MP.
More changing-base questions are covered in Successive Profit and Loss Changes.
8. Successive Percentage Change Formula
For two percentage changes a% and b%, use:
Net change% = a + b + ab/100
Treat an increase as positive and a decrease as negative.
Example: 20% increase followed by 10% decrease:
20 + (−10) + (20 × −10)/100 = 8% increase.
Formula use is safest when the sign convention is kept clear.
9. Ratio Forms of Common Profit and Loss Percentages
- 20% profit → SP:CP = 120:100 = 6:5
- 25% profit → SP:CP = 125:100 = 5:4
- 10% loss → SP:CP = 90:100 = 9:10
- 20% loss → SP:CP = 80:100 = 4:5
- 25% loss → SP:CP = 75:100 = 3:4
Ratios are especially useful when values are proportional or when a full percentage equation would be unnecessarily long. For speed methods, see Profit and Loss Tricks for Faster Solving.
10. Formula Selection Guide
- CP and SP given → first find profit or loss amount.
- CP and profit/loss% given → use direct SP formula.
- SP and profit/loss% given → use reverse CP formula.
- MP and discount% given → find SP from MP.
- SP and discount% given → reverse the discount to find MP.
- Two successive percentage changes → use multipliers or the signed net-change formula.
Before applying any formula, identify the base. That one step prevents most formula-selection errors.
11. Worked Formula Examples
Example 1: CP = ₹250, SP = ₹300. Profit = ₹50. Profit% = 50 ÷ 250 × 100 = 20%.
Example 2: MP = ₹640, SP = ₹544. Discount = ₹96. Discount% = 96 ÷ 640 × 100 = 15%.
Example 3: SP = ₹540 at 10% loss. CP = 540 × 100 ÷ 90 = ₹600.
Example 4: CP = ₹1,200 and profit = 15%. SP = 1,200 × 115 ÷ 100 = ₹1,380.
12. Common Formula Mistakes
- Wrong denominator: using SP instead of CP for ordinary profit% or loss%.
- Wrong discount base: discount% normally uses MP, not CP.
- Direct reversal: subtracting the same percentage from SP to recover CP.
- Adding successive percentages blindly: the base changes after the first percentage change.
- Using a formula without checking the question type: first decide whether the unknown is CP, SP, MP, profit, loss or discount.
For a dedicated error-repair lesson, read Common Profit and Loss Mistakes.
13. Quick Revision Formula Sheet
- Profit = SP − CP
- Loss = CP − SP
- Profit% = Profit/CP × 100
- Loss% = Loss/CP × 100
- SP at profit = CP × (100 + p)/100
- SP at loss = CP × (100 − p)/100
- CP at profit = SP × 100/(100 + p)
- CP at loss = SP × 100/(100 − p)
- Discount = MP − SP
- Discount% = Discount/MP × 100
- Effective successive discount = a + b − ab/100
14. Practice Check
- CP = ₹500, SP = ₹625. Find profit%.
- CP = ₹900, loss = 20%. Find SP.
- SP = ₹960 at 20% profit. Find CP.
- MP = ₹1,500, discount = 12%. Find SP.
- Find the effective discount for successive discounts of 15% and 10%.
Answers: (1) 25%; (2) ₹720; (3) ₹800; (4) ₹1,320; (5) 23.5%.
15. Next Step
If the formulas are clear but calculation speed is still slow, move to Profit and Loss Tricks for Faster Solving. If the basic meaning of CP, SP and percentage base is still uncertain, revise Profit and Loss Basics.
For the complete topic map, return to the Profit and Loss Master Guide. After revision, test the formulas in Profit and Loss Practice Set 1.