Profit, Loss, Discount

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DEFINITIONS:-

⇒ Cost price (C.P.):-The price at which an article is purchased, is called its cost price.

⇒ Selling price (S. P) :- The price at which an article is sold, is called its selling price.

⇒ Profit or Gain :- If S.P. > C.P. then the seller is said to have a Profit or Gain.

⇒ Loss :- If S.P. < C.P., then the seller is said to have incurred a loss.

⇒ Profit :- S.P. – C.P.

⇒ Loss :- C.P. – S.P.

FORMULAE:-

percent sign space Profit space equals space fraction numerator Profit space cross times space 100 over denominator straight C. straight P. end fractionpercent sign space Loss space equals space fraction numerator Loss space cross times space 100 over denominator straight C. straight P. end fraction

straight S. straight P. space equals space open parentheses fraction numerator 100 space plus space Profit space percent sign over denominator 100 end fraction close parentheses space cross times space straight C. straight P.straight S. straight P. space equals space open parentheses fraction numerator 100 space minus space Loss space percent sign over denominator 100 end fraction close parentheses space straight C. straight P.

straight C. straight P. space equals space open parentheses fraction numerator 100 over denominator 100 space plus space Gain space percent sign end fraction close parentheses space cross times space straight S. straight P.

straight C. straight P. space equals space open parentheses fraction numerator 100 over denominator 100 space minus space Loss space percent sign end fraction close parentheses space cross times space straight S. straight P.

⇒ If an article is continuously sold with a profit or loss (r%), then

then final price paid by D space equals space open parentheses fraction numerator 100 space plus-or-minus space straight r subscript 1 over denominator 100 end fraction close parentheses open parentheses fraction numerator 100 space plus-or-minus space straight r subscript 2 over denominator 100 end fraction close parentheses open parentheses fraction numerator 100 space plus-or-minus space straight r subscript 2 over denominator 100 end fraction close parentheses

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

Loss % = open parentheses fraction numerator Common space loss space and space Gain space percent sign over denominator 10 end fraction close parentheses squared space equals space open parentheses straight x over 10 close parentheses squared

⇒ If a trader professes to sell his goods at cost price, but uses false weights, then

Gain % = open square brackets open parentheses fraction numerator Error over denominator True space value space minus space Error end fraction close parentheses space cross times space 100 close square brackets space percent sign

 

 

⇒ If r1 % profit → at the time of purchased

r2 % profit → at the time of selling

% profit = r1 + r2 + fraction numerator straight r subscript 1 straight r subscript 2 over denominator 100 end fraction

⇒ When the selling price of the two articles are equal, then

CP1 : CP2 = (100 ± r2) : (100 ± r1)

⇒ If 'a' articles are bought for Rs. 6 and 'c' articles are sold for Rs. d, then

a) % Profit = open parentheses fraction numerator bc space �

⇒ If a articles are bought for Rs. 'b' and b articles are sold for Rs. 'a', then

% Profit = open parentheses fraction numerator straight b squared space �

⇒ Marked price  = (M.P.)

⇒ Selling price = (S.P.)

⇒ Discount = Marked price – selling price

⇒ % Discount = fraction numerator marked space price space minus space selling space price space over denominator marked space praice end fraction × 100 

⇒ When discount given two times, then

Unique discount = D1 + D2fraction numerator straight D subscript 1 straight D subscript 2 over denominator 100 end fraction

⇒ If we sold an article at D% discount, then profit or loss is r%, then

MP over CP space equals space fraction numerator 100 space plus-or-minus space straight r over denominator 100 space minus space straight D end fraction

⇒ When an article sold out at without any discount, then

% profit or loss = open parentheses fraction numerator straight D space plus-or-minus space straight r over denominator 100 space minus space straight D end fraction close parentheses space cross times space 100

⇒ If discount is given in the form of 'x' articles are given free then

% Discount = fraction numerator straight y space cross times space 100 over denominator straight x space plus space straight y end fraction

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