FORMULAE




Profit and Loss


  1. Cost price = price at which the item is made
  2. Selling price = price at which item is sold.
  3. Gain = If SP > CP then SP - CP.
  4. Loss = If CP > SP then CP - SP.
  5. Percentage profit = ( Profit * 100) / CP
  6. Percentage loss = ( Loss * 100) / CP
  7. SP = ( 100 + Gain% ) * CP / 100
  8. SP = ( 100 - Loss% ) * CP / 100
  9. CP = 100 * SP / ( 100 + Gain% )
  10. CP = 100 * SP / ( 100 - Loss% )




Calculating the percentage profit on basis of amount earned:


Suppose a trader recovers cost of 25 clothes by selling 20 clothes then the percentage profit?


%profit = ( Goods left / Goods sold ) * 100 = ( 5 / 20 ) * 100 = 25%


Calculating %loss when two items are sold at same value of profit and loss respectively:


Suppose I sell two items, one at profit of 10% and other at loss of 10% then I shall always have a loss of [ x / 10 ]2 % = ( 10 / 10 )2 = 1% loss





Practice Exercise: Profit and Loss
Click here



Percentage


If the price of a commodity increases by R%, then the reduction in consumption so  as not to increase the expenditure is




New consumption = [R / ( 100 + R )) * 100] %


If the price of the commodity decreases by R%,then the increase in consumption so as to decrease the expenditure is 

New expenditure = [ ( R / ( 100 - R ) * 100] %

Results on Population : Let the population of the town be P now and suppose it increases at the rate of    
       R% per annum, then : 



Population after n years = P * [1+(R/100)]^n
Population n years ago = P / [1+(R/100)]^n


Results on Depreciation :  Let the present value of a machine be P. Suppose  it depreciates  at the rate 
       R% per annum.

Value of the machine after n years = P * [1-(R/100)]^n
Value of the machine n years ago = P / [1-(R/100)]^n


Practice Exercise: Percentages
Click here




Partnership Theory


When A and B are partners and both invest in a ratio say x:y but at the same time then their ratio of profits sharing is same as their investment ratio i.e. x:y.


However if A invests 'x' amount for 'p' months and B invests 'y' amount for 'q' months then their share in profits is:




A's share : B's share = x * p : y * q


Practice Exercise: Partnership Theory
Click here



Laws of Indices:


(i) aᵐ ∙ aⁿ = aᵐ + ⁿ


(ii) aᵐ/aⁿ = aᵐ - ⁿ

(iii) (aᵐ)ⁿ = aᵐ * ⁿ

(v) a-ⁿ = 1/aⁿ

(vi) ⁿ√aᵐ = aᵐ/ⁿ


(vii) (ab)ᵐ = aᵐ ∙ bⁿ.

(viii) (a/b)ᵐ = aᵐ/bm



Equations


  • A∪B = n(A) + n(B) - n(A∩B) and 
                if A∩B = not empty then n(A-B) + n(B-A) + n(A∩B)
  • n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) -n(A∩C) + n(A∩B∩C)




Practice Exercise: Linear equations
Click here