₹ Profit & Loss · complete formulas & shortcuts
IBPS PO · SSC CGL Railway · Campus | ✓ 12+ shortcut formulas
Quick Note
Every year, thousands of aspirants prepare for banking, SSC, railway, and other government exams where profit and loss questions are a staple of the quantitative aptitude section. Whether you're aiming for IBPS PO, SSC CGL, or any other competitive exam, mastering profit and loss formulas can significantly boost your overall score.
▣ Introduction: Why Profit and Loss Matters
The beauty of profit and loss lies in its practical applicability. From calculating discounts during festive sales to understanding business profitability, these concepts are everywhere. In exams, however, the challenge isn't just knowing the formulas—it's applying them accurately and quickly under time pressure.
This comprehensive guide covers everything from basic concepts to advanced shortcut techniques, complete with solved examples that mirror actual exam patterns.
▣ Understanding Core Terminology
Before diving into formulas, let's establish a clear understanding of the fundamental terms you'll encounter.
Cost Price (CP)
Definition: The price at which an article is purchased. This is your base price for all calculations.
- Fixed Cost: Remains constant regardless of quantity
- Variable Cost: Changes based on the number of units purchased
Selling Price (SP)
Definition: The price at which an article is sold to the customer.
Profit or Gain
Definition: Occurs when Selling Price exceeds Cost Price.
Profit = SP − CP
Loss
Definition: Occurs when Cost Price exceeds Selling Price.
Loss = CP − SP
Marked Price (MP)
Definition: The price listed or tagged on an article before any discount is applied.
Discount
Definition: The reduction offered on the Marked Price.
Discount = MP − SP
▣ Complete Profit and Loss Formulas
Core Formulas
| Concept | Formula |
|---|---|
| Profit | SP − CP |
| Loss | CP − SP |
| Profit Percentage | (Profit / CP) × 100% |
| Loss Percentage | (Loss / CP) × 100% |
Selling Price Formulas
SP = CP × (100 + Profit%) / 100
SP = CP × (100 − Loss%) / 100
Cost Price Formulas
CP = SP × 100 / (100 + Profit%)
CP = SP × 100 / (100 − Loss%)
⚠️ Important Note:
Profit and loss percentages are always calculated on Cost Price (CP) unless otherwise stated.
▣ Advanced Formulas and Shortcut Tricks
1. Equal SP with Equal Profit and Loss
When a person sells two similar items at the same SP, one at a profit of x% and the other at a loss of x%, there's always an overall loss.
Loss% = (x/10)²
Example:
If two items are sold at ₹600 each, one at 20% profit and one at 20% loss:
Loss% = (20/10)² = 4%
2. False Weight Formula
When a shopkeeper uses false weights to cheat customers:
Gain% = [Error / (True Value − Error)] × 100%
Where Error = True Weight − False Weight
Example:
If a shopkeeper uses 900gm instead of 1000gm:
Gain% = 100/900 × 100 = 11.11%
3. Successive Profit/Loss Formula
Two successive profits of x% and y%:
Net Profit% = x + y + (xy/100)
Profit of x% and loss of y%:
Net Profit/Loss% = x − y − (xy/100)
Note: For profit, take positive values; for loss, take negative values.
4. CP of x articles = SP of y articles
Profit% = [(x − y) / y] × 100
5. Discount Formulas
Discount% = (Discount / MP) × 100
SP = MP × (100 − Discount%) / 100
6. Equivalent Loss When P% = L%
Loss% = P² / 100
▣ Quick Reference: All Formulas at a Glance
| # | Formula |
|---|---|
| 1 | Profit = SP − CP |
| 2 | Loss = CP − SP |
| 3 | Profit% = (Profit/CP) × 100 |
| 4 | Loss% = (Loss/CP) × 100 |
| 5 | SP (with profit) = CP × (100 + P%) / 100 |
| 6 | SP (with loss) = CP × (100 − L%) / 100 |
| 7 | CP (with profit) = SP × 100 / (100 + P%) |
| 8 | CP (with loss) = SP × 100 / (100 − L%) |
| 9 | Discount = MP − SP |
| 10 | Discount% = (Discount/MP) × 100 |
| 11 | Equal SP with equal P and L: Loss% = (P/10)² |
| 12 | False weight: Gain% = [Error / (True Value − Error)] × 100 |
▣ Solved Examples for Practice
Example 1: Basic Profit Calculation
Question: A shopkeeper buys 1kg apples for ₹100 and sells them for ₹120. Find the profit percentage.
Solution:
- CP = ₹100
- SP = ₹120
- Profit = 120 − 100 = ₹20
- Profit% = (20/100) × 100 = 20%
Example 2: Finding CP from SP
Question: A table is sold for ₹5060 at a profit of 10%. Find the Cost Price.
Solution:
- SP = ₹5060
- Profit% = 10%
- CP = SP × 100 / (100 + Profit%)
- CP = 5060 × 100 / 110 = ₹4600
Example 3: Equal SP with Different Profit and Loss
Question: Two articles are sold at ₹500 each. One at 25% profit and the other at 25% loss. Find the overall profit or loss percentage.
Solution:
- Profit and loss percentages are equal (25%)
- Loss% = (25/10)² = 625/100 = 6.25% loss
Example 4: Successive Discounts
Question: A T-shirt with marked price ₹200 is sold after two successive discounts of 20% each. Find the final selling price.
Solution:
- Effective discount = 20 + 20 − (20 × 20/100) = 36%
- Discount = 200 × 36/100 = ₹72
- SP = 200 − 72 = ₹128
Alternative Method:
- After first discount: 200 × 0.80 = ₹160
- After second discount: 160 × 0.80 = ₹128
Example 5: CP of x articles = SP of y articles
Question: If the cost price of 5 oranges equals the selling price of 4 oranges, find the profit percentage.
Solution:
- Let CP of 1 orange = ₹4
- Then CP of 5 oranges = ₹20
- SP of 4 oranges = ₹20
- SP of 1 orange = ₹5
- Profit% = (5−4)/4 × 100 = 25%
Example 6: False Weight Problem
Question: A shopkeeper claims to sell goods at cost price but uses 900gm instead of 1000gm. Find his profit percentage.
Solution:
- Error = 1000 − 900 = 100gm
- Gain% = 100/900 × 100 = 11.11%
Example 7: Successive Selling with Profit
Question: A sells an article to B at 20% profit, and B sells it to C at 10% profit. If C pays ₹264, find the original cost price.
Solution:
- Let original CP = x
- Price at B = x × (120/100) = 1.2x
- Price at C = 1.2x × (110/100) = 1.32x
- 1.32x = 264
- x = ₹200
Example 8: Loss Percentage Problem
Question: A man sold a horse at a loss of 10%. If he had sold it for ₹60 more, he would have gained 20%. Find the CP.
Solution:
- Let CP = x
- SP₁ = 0.9x (10% loss)
- SP₂ = 1.2x (20% profit)
- 1.2x − 0.9x = 60
- 0.3x = 60
- x = ₹200
▣ Common Mistakes to Avoid
1. Wrong Base for Percentage Calculation
Always calculate profit and loss percentages on Cost Price, not Selling Price, unless specifically stated otherwise.
2. Confusing Profit and Loss Scenarios
Carefully check whether SP > CP (profit) or CP > SP (loss) before applying formulas.
3. Forgetting Discount Application
Remember that discounts are applied on Marked Price, not Cost Price.
4. Mistakes in Successive Calculations
When applying successive discounts, don't simply add percentages—use the formula x + y − xy/100.
5. Overlooking Additional Costs
Transportation, packing, and other overhead costs must be included in CP.
▣ Practice Questions for Self-Assessment
Question 1
A man buys a fan for ₹1000 and sells it at a loss of 15%. What is the selling price?
Solution:
SP = 1000 × (100−15)/100 = ₹850
Question 2
A shopkeeper allows a discount of 10% on the marked price and still gains 17%. What percentage above CP did he mark his goods?
Solution:
Let CP = 100, SP = 117. If MP = x, then 0.9x = 117, so x = 130.
Marked 30% above CP
Question 3
A dishonest merchant sells goods using weights 15% less than true weights and still manages 20% profit. Find total gain percentage.
Solution:
False weight = 850gm, True = 1000gm. Cost = ₹850, SP = 120% of 1000 = ₹1200.
Gain = 350/850 × 100 = 41.17%
Question 4
By selling 100 notebooks, a shopkeeper gains the SP of 20 notebooks. Find the gain percentage.
Solution:
Let SP of 1 notebook = ₹1. SP of 100 = ₹100. Gain = ₹20, CP = ₹80.
Gain% = 20/80 × 100 = 25%
▣ Tips for Exam Success
1. Memorize key formulas
Create a formula sheet and review it regularly.
2. Practice mental math
Speed is crucial—develop quick calculation skills.
3. Identify question type
Recognize patterns—is it false weight, successive discounts, or equal SP?
4. Use shortcut methods
Apply formulas like (x/10)² for equal P and L to save time.
5. Read carefully
Pay attention to whether the question asks for CP, SP, or percentage.
6. Double-check calculations
Avoid careless errors, especially with decimal places.
▣ Frequently Asked Questions
Q: What is the base for calculating profit and loss percentage?
Profit and loss percentages are always calculated on Cost Price (CP) unless specifically stated otherwise.
Q: What happens when two items are sold at the same SP with equal profit and loss?
There is always an overall loss given by the formula Loss% = (P/10)².
Q: How is false weight profit calculated?
Using the formula Gain% = [Error / (True Value − Error)] × 100%.
Q: Can I use successive discount formula for losses?
Yes. For two successive losses of x% and y%, use −x − y + (xy/100).
🏁 Conclusion
Profit and loss is a high-scoring topic in competitive exams. With a solid grasp of formulas and shortcut techniques, you can solve these questions quickly and accurately.
Remember these golden rules:
- Base percentage on Cost Price
- Practice diverse problem types
- Use shortcuts wisely
- Avoid common mistakes
Ready to test your skills?
Download practice sets and take mock tests to evaluate your preparation level. Success in profit and loss questions comes from understanding concepts, memorizing formulas, and regular practice.
Last Updated: June 2026
Good luck with your competitive exam preparation! 🚀
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