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__PROFIT AND LOSS__

**Points to Remember:**

**Cost Price (CP):** The price, at which an article is brought, including all costs such as transportation, taxes, etc.

**Selling Price (SP):** The price at which an article is sold.

**Profit or Gain:** If selling price is greater than cost price, the seller makes profit or gain. Gain = SP – CP.

**Loss:** If the SP is less than the CP then seller makes loss. Loss = CP – SP

**Basic Formulae: **

i) Gain = SP – CP

ii) Loss = CP – SP

iii) Gain% = {[(SP – CP) x 100]/CP}

iv) Loss% = {[(CP – SP) x 100]/CP}

v) A person sells an item at x% loss (- sign) or x% profit (+sign). Had he sold that item for Rs. X more his profit would have been y%. Then

**CP = [X/(y±x) × 100)**

vi) If there is a loss of x% on selling an item at selling price (SP1) and also there is a profit of y% on selling price (SP2) then

**SP2 = [SP1(100 + y)/(100 – x)]**

vii) When a person sells two similar items, one at a gain of say x%, and at a loss of x%, then the seller always incurs a loss given by:

**Loss% = (Common Loss and Gain%/10)2 = (x/10)2**

viii) If a trader professes to sell his goods at CP, but uses false weights, then,

**Gain% = [Error/(True value – error)]x100%**

ix) If the Cost price of M articles is equal to the selling price of N articles then the profit percent is given by

**P = [(M – N)/N] x 100**

**Marked Price or List Price:** Price that is indicated or marked on the article is called marked price or MP.

**Discount:** It is reduction given on the Marked Price or List Price of an article.

**Discount% = discount/MP x 100%;**

**Selling Price = (100 – d)/100 x MP**

x) If a trader gets x% profit and x% loss in selling two different articles, then in overall transaction, there is always loss which is given by

**Loss% = (x/2)2**

xi) If an article is sold after allowing two successive discounts of d1% and d2% then selling price (S.P) is given by

**S.P = [(100 – d1)/100] x [(100 – d2)/100] x MP**

xii) Two successive discounts of d1 and d2 are equivalent to a single discount of

**d = d1 + d2 – (d1 x d2/100)**