Company LogoCompany Logo
Company LogoCompany Logo
Back to Quantitative

Profit And Loss

    • Theory
    • Set 1
    • Set 2
    • Set 3
    • Set 4
    • Set 1
    • Set 2
  1. Aptitude
  3. Quantitative
  5. Profit and Loss
  7. Theory

Profit and Loss: Concepts, Formulas, and Clear Examples

CP (cost price) and SP (selling price) drive profit =SP−CP=SP-CP=SP−CP and loss =CP−SP=CP-SP=CP−SP. Percent always on CP unless stem says on SP.

Successive discounts multiply on marked price; false weights scale effective CP.

Partnership with dishonest dealer: actual CP vs claimed weight.

Basic profit percent

Profit %

Profit%=SP−CPCP×100\text{Profit\%} = \frac{SP-CP}{CP}\times100Profit%=CPSP−CP​×100

SP from profit%

SP=CP(1+p100)SP = CP\left(1+\frac{p}{100}\right)SP=CP(1+100p​)

Example — 20% profit

CP=250, profit 20%. SP = 250×1.2=300250\times1.2=300250×1.2=300.

Loss and reverse CP

Loss %

CP−SPCP×100\frac{CP-SP}{CP}\times100CPCP−SP​×100

CP from SP

CP=SP1±p/100CP = \frac{SP}{1\pm p/100}CP=1±p/100SP​

Marked price and discount

After discount d%

SP=MP(1−d100)SP = MP\left(1-\frac{d}{100}\right)SP=MP(1−100d​)

Two discounts

SP=MP(1−d1100)(1−d2100)SP = MP\left(1-\frac{d_1}{100}\right)\left(1-\frac{d_2}{100}\right)SP=MP(1−100d1​​)(1−100d2​​)

False weights

Seller uses weight w instead of W

Actual CP per true kg=nominal CP×Ww\text{Actual CP per true kg} = \frac{\text{nominal CP}\times W}{w}Actual CP per true kg=wnominal CP×W​

Break even

  • SP = CP + overheads when given.
  • 0% profit at SP equal to total cost.

Exam traps

  • Profit% on SP wording changes denominator.
  • Compare CP before deciding cheaper deal.

Step-by-step method for exam questions

  1. Label CP, SP, MP, discount, profit/loss %.
  2. Convert % to multiplier on correct base.
  3. Chain discounts on MP.
  4. Adjust CP for false weight if any.
  5. Compute numeric SP/CP/profit.
  6. Select option.

Formula cheat sheet

SituationFormulaWhen to use
Profit p% on CPSP=CP(1+p/100)SP=CP(1+p/100)SP=CP(1+p/100)Standard
Loss l% on CPSP=CP(1−l/100)SP=CP(1-l/100)SP=CP(1−l/100)Loss sale
Find CP from SPCP=SP/(1±p/100)CP=SP/(1\pm p/100)CP=SP/(1±p/100)Reverse
Discount on MPSP=MP(1−d/100)SP=MP(1-d/100)SP=MP(1−d/100)Marked price
False weightEffective CP scalesShort weight

Frequently asked questions

Profit% on SP?

Use (SP−CP)/SP(SP-CP)/SP(SP−CP)/SP when explicitly on SP.

10% off then 10% off?

Net 19% off MP, not 20%.

Same SP, different CP?

Higher CP ⇒ lower profit%.

GST in stem?

Follow whether tax included in SP/CP labels.

Practice on this platform

Use 4 practice sets (10 MCQs, detailed solution after each answer) and 2 timed mocks (20 minutes) on this topic to convert formulas into speed and accuracy.

Start practiceAll Quantitative topics