Profit and Loss

Cost Price (CP): The price at which an item is purchased.

Selling Price (SP): The price at which the item is sold.

Profit (P): When SP > CP, the seller earns a profit.

Loss (L): When SP < CP, the seller incurs a loss.

Profit Percent (P%) and Loss Percent (L%) measure how much profit or loss is made relative to the cost price.

Key Definitions

Term	Meaning
Cost Price (CP)	The original price at which an item is purchased by the seller
Marked Price (MP)	The price labeled or displayed on the item before any discount
Discount	A reduction offered on the marked price, usually expressed as a percentage
Selling Price (SP)	The final price after discount, before VAT
VAT (Value Added Tax)	A government-imposed tax added to the selling price (commonly 13%)
SP with VAT	The total amount paid by the buyer, including VAT

Price Flow: CP → MP → Discount → SP → SP with VAT

1. Start with Cost Price (CP)
2. Add markup to get Marked Price (MP)
3. Apply discount to get Selling Price (SP)
4. Add VAT to get SP with VAT (final payable amount)

Formulas

• Profit: $P = SP - CP$

• Loss: $L = CP - SP$

• Profit Percent: $P\% = \dfrac{P}{CP} \times 100\% = \dfrac{SP - CP}{CP} \times 100\%$

• Loss Percent: $L\% = \dfrac{L}{CP} \times 100\% = \dfrac{CP - SP}{CP} \times 100\%$

• Price relations: $SP = CP + P$

  $SP = CP - L$

• Amount from percent: $P = CP \times \dfrac{P\%}{100}$

  $L = CP \times \dfrac{L\%}{100}$

• Discount Amount = $\dfrac{\text{Discount \%}}{100} \times \text{MP}$

• SP = $\text{MP} - \text{Discount Amount}$

• VAT Amount = $\dfrac{\text{VAT \%}}{100} \times \text{SP}$

• SP with VAT = $\text{SP} + \text{VAT Amount}$

Tips and Tricks

• Read the question carefully. Identify which values are given: CP, MP, SP, profit (P), loss (L), profit% (P%) or loss% (L%).

• Beware which base the percent uses:

  • Profit% and Loss% are normally relative to CP: P% = P/CP × 100.

• For successive percentage changes, multiply factors (do not add/subtract percents):

  • Example: increase 10% then decrease 10% → net factor = 1.10 × 0.90 = 0.99 → 1% loss overall.

• For multiple transactions, work with totals:

  • Overall profit% = (Total SP − Total CP) / Total CP × 100.

• Use ratios to avoid decimals:

  • Keep 1 / 3 instead of replacing with 33% until the end.

• Fast sanity checks:

  • If SP > CP → profit; if SP < CP → loss.

Keep these patterns in mind and translate words into one of these formula forms before calculating.