### 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

### 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 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

### Partnership Theory

hen 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

### 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)