Profit & Loss Formula Cheat Sheet

Profit & Loss Formula Cheat Sheet

Profit & Loss questions are based mainly on the relationship between Cost Price (CP) and Selling Price (SP).

The most important rule to remember:

Unless stated otherwise, Profit% and Loss% are calculated on Cost Price (CP).

1. Basic Terms

2. Basic Profit & Loss Formulas

Profit

Profit = SP − CP

Loss

Loss = CP − SP

Profit Percentage

Profit % = (Profit / CP) × 100

Loss Percentage

Loss % = (Loss / CP) × 100

3. Find Selling Price

When Profit is Given

If profit is p%:

SP = CP × (100 + p) / 100

When Loss is Given

If loss is l%:

SP = CP × (100 − l) / 100

Example

CP = ₹800 Profit = 25%

SP = 800 × 125/100
   = ₹1,000

4. Find Cost Price

When Profit is Given

CP = SP × 100 / (100 + Profit%)

When Loss is Given

CP = SP × 100 / (100 − Loss%)

Example

An item is sold for ₹1,200 at 20% profit.

CP = 1200 × 100/120
   = ₹1,000

5. CP–SP Ratio Shortcut

If profit is p%:

CP : SP = 100 : (100 + p)

Example: 25% profit

CP : SP = 100 : 125
        = 4 : 5

If loss is l%:

CP : SP = 100 : (100 − l)

Example: 20% loss

CP : SP = 100 : 80
        = 5 : 4

This ratio method is often faster than using actual values.

6. Profit/Loss from CP and SP Ratio

If:

CP : SP = a : b

and b > a:

Profit % = [(b − a) / a] × 100

If a > b:

Loss % = [(a − b) / a] × 100

Example

CP : SP = 5 : 6

Profit % = (1/5) × 100
         = 20%

7. Marked Price and Discount

Discount is normally calculated on Marked Price (MP).

Discount = MP − SP

Discount Percentage

Discount % = (Discount / MP) × 100

Selling Price After Discount

If discount = d%:

SP = MP × (100 − d) / 100

Example

MP = ₹2,000 Discount = 15%

SP = 2000 × 85/100
   = ₹1,700

8. Find Marked Price

If Selling Price and discount percentage are known:

MP = SP × 100 / (100 − Discount%)

Example

An item is sold for ₹800 after a 20% discount.

MP = 800 × 100/80
   = ₹1,000

9. Successive Discounts

If two successive discounts are a% and b%:

Equivalent Discount
= a + b − (ab / 100)

Example

20% discount followed by 10% discount:

Equivalent Discount
= 20 + 10 − (20 × 10)/100
= 30 − 2
= 28%

So:

20% + 10% successive discounts
= 28% overall discount

Important: Successive discounts are not simply added.

10. Three Successive Discounts

For discounts a%, b%, and c%, the safest quick method is the multiplier method:

Final SP
= MP × (100−a)/100
     × (100−b)/100
     × (100−c)/100

Then:

Equivalent Discount %
= [(MP − Final SP) / MP] × 100

Example

Discounts of 10%, 20%, and 25%:

Remaining value
= 0.90 × 0.80 × 0.75
= 0.54

Therefore:

Equivalent Discount
= 100% − 54%
= 46%

11. Markup and Discount Together

Suppose an article is marked m% above CP and a discount of d% is offered.

MP = CP × (100 + m)/100

Then:

SP = CP × (100 + m)/100 × (100 − d)/100

Net profit/loss percentage:

Net % = [(SP − CP) / CP] × 100

Positive result = Profit Negative result = Loss

12. Markup + Discount Shortcut

If price is increased by m% and then decreased by d%:

Net Change %
= m − d − (md / 100)

Example

Marked 25% above CP and discount = 10%.

Net Change
= 25 − 10 − (25 × 10)/100
= 15 − 2.5
= 12.5%

Therefore:

Profit = 12.5%

13. Required Markup for a Desired Profit

If a shopkeeper wants p% profit even after giving d% discount:

MP / CP
= (100 + p) / (100 − d)

Therefore:

Markup %
= [(100 + p)/(100 − d) × 100] − 100

Example

Desired profit = 20% Discount = 20%

MP / CP = 120/80
        = 1.5

So MP must be:

150% of CP

Therefore:

Markup = 50%

14. Same Selling Price: One Profit, One Loss

A very common competitive-exam question:

Two articles are sold at the same selling price.

One is sold at x% profit and the other at x% loss.

Then there is always an overall loss.

Overall Loss % = x² / 100

Example

One item is sold at 20% profit and another at 20% loss, both at the same SP.

Overall Loss
= 20² / 100
= 4%

Answer: 4% loss

Important Condition

This shortcut works when:

• profit percentage = loss percentage, and
• both articles have the same Selling Price.

15. Same Cost Price: Equal Profit and Loss %

If two articles have the same Cost Price, and:

• one is sold at x% profit
• another at x% loss

then:

Overall Profit/Loss = 0%

Example

Each article costs ₹1,000.

First:

20% profit → SP = ₹1,200

Second:

20% loss → SP = ₹800

Total:

Total CP = ₹2,000
Total SP = ₹2,000

Therefore:

No Profit, No Loss

Do not confuse this with the same selling price case.

16. Profit Based on Selling Price

Sometimes a question says:

Profit is x% of Selling Price.

This is different from normal profit percentage.

If:

Profit = x% of SP

then:

CP = SP × (100 − x)/100

Normal Profit% on CP becomes:

Profit % on CP
= [x / (100 − x)] × 100

Example

Profit is 20% of SP.

Normal Profit %
= 20/80 × 100
= 25%

17. Profit Based on Cost Price vs Selling Price

Profit = x% of CP

Normal profit percentage:

Profit % = x%

Profit = x% of SP

Equivalent profit percentage on CP:

= [x / (100 − x)] × 100

Quick Conversion

18. Loss Based on Selling Price

If loss is x% of SP:

CP = SP × (100 + x)/100

Normal Loss% on CP:

Loss % on CP
= [x / (100 + x)] × 100

Example

Loss is 25% of SP.

Loss % on CP
= 25/125 × 100
= 20%

19. False Weight / Dishonest Dealer

Suppose a shopkeeper charges the price of 1 kg but gives only w grams.

Assuming goods are sold at the cost-price rate:

Profit %
= [(1000 − w) / w] × 100

Example

A dealer charges for 1 kg but gives only 800 g.

Profit %
= (200 / 800) × 100
= 25%

20. False Weight General Formula

If a dealer claims to give A units but actually gives B units:

Profit %
= [(A − B) / B] × 100

This formula assumes the dealer charges the cost-price rate for the claimed quantity.

21. False Weight + Markup

If a dealer:

• sells at p% above cost price, and
• gives w grams instead of 1000 grams,

then:

Revenue for claimed 1 kg
= CP of 1 kg × (100 + p)/100

Actual cost corresponds to only w grams.

A useful multiplier is:

Profit Multiplier
= (100 + p)/100 × 1000/w

Therefore:

Profit %
= (Profit Multiplier − 1) × 100

Example

10% above CP and 900 g instead of 1 kg:

Multiplier
= 1.10 × 1000/900
= 11/9

Therefore:

Profit %
= (11/9 − 1) × 100
= 22.22%

22. Profit When SP Changes

Suppose an article sold at SP₁ gives a profit/loss, and changing the selling price to SP₂ changes the profit/loss.

The key relation is:

Difference in SP
= Difference in Profit/Loss Amount

This is useful in questions such as:

Selling an article for ₹500 causes a 10% loss, while selling it for ₹600 gives...

First find CP:

CP = 500 × 100/90

Then calculate the new profit percentage normally.

23. Difference Between Two Selling Prices

If selling at ₹A gives x% loss and selling at ₹B gives y% profit:

B − A
= CP × (x + y)/100

Therefore:

CP = (B − A) × 100 / (x + y)

Example

At ₹800 → 20% loss At ₹1,100 → 10% profit

Difference in SP = 300

CP = 300 × 100 / (20 + 10)
   = ₹1,000

24. Required SP for Changing Loss into Profit

If an article is currently sold at x% loss and you want y% profit:

Current SP:

SP₁ = CP × (100 − x)/100

Required SP:

SP₂ = CP × (100 + y)/100

Therefore:

SP₂ / SP₁
= (100 + y)/(100 − x)

This ratio can solve many questions without finding CP.

25. Increase in SP Needed to Turn Loss into Profit

If current loss = x% and desired profit = y%:

Required Increase %
= [(x + y)/(100 − x)] × 100

Example

An article is sold at 20% loss. By what percentage should its current SP be increased to earn 20% profit?

Required Increase
= (20 + 20)/80 × 100
= 50%

26. Decrease in SP to Change Profit into Loss

If current profit = x% and desired loss = y%:

Required Decrease %
= [(x + y)/(100 + x)] × 100

Example

Current profit = 25% Desired loss = 20%

Required Decrease
= 45/125 × 100
= 36%

27. Goods Bought/Sold in Quantity

For questions such as:

Buy 10 articles for ₹100 and sell 8 articles for ₹100.

Use unit prices.

Cost per Article

CP per article
= Total Cost / Number Bought

Selling Price per Article

SP per article
= Total Selling Price / Number Sold

Then:

Profit/Loss %
= [(SP − CP)/CP] × 100

Example

Buy 10 for ₹100:

CP per article = ₹10

Sell 8 for ₹100:

SP per article = ₹12.50

Therefore:

Profit %
= 2.5/10 × 100
= 25%

28. Fast Multiplier Method

For exam calculations, percentage multipliers are often faster.

Example:

CP = ₹800
Profit = 25%

SP = 800 × 1.25
   = ₹1,000

29. One-Minute Revision Table

30. Common Exam Mistakes

1. Calculating Profit% on SP

Normally:

Profit % = Profit / CP × 100

not:

Profit / SP × 100

unless the question explicitly says profit is a percentage of SP.

2. Calculating Discount on CP

Discount is normally calculated on Marked Price:

Discount % = Discount / MP × 100

3. Adding Successive Discounts

20% + 10%

does not mean 30% total discount.

Correct:

20 + 10 − (20×10)/100
= 28%

4. Assuming Equal Profit and Loss Cancel

20% profit and 20% loss do not always cancel.

Check whether the question gives:

• same CP, or
• same SP.

5. Confusing Markup with Profit

Markup is based on CP when MP is set:

Markup = MP − CP

But actual profit depends on the final SP after discount.

6. Using the False-Weight Shortcut Without Checking Conditions

The simple false-weight formula assumes the dealer charges the price corresponding to the claimed quantity at the cost-price rate. If markup or discount is also involved, include those changes separately.

31. Exam Quick Tips

• Treat CP = 100 when only percentages are given.
• Use ratios instead of actual values whenever possible.
• Use multipliers for combined markup, discount, profit, and loss questions.
• Remember: Profit/Loss → CP is usually the base.
• Remember: Discount → MP is the base.
• For successive discounts, multiply the remaining percentages.
• For same-SP equal-profit/equal-loss questions, remember x²/100 loss.
• In quantity questions, first convert everything to cost per unit and selling price per unit.
• Read carefully whether a percentage is based on CP, SP, or MP.

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