FORMULAE: Profit and Loss

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] %

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:

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/b^m

Equations

• A∪B = n(A) + n(B) - n(A∩B) and 

• n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) -n(A∩C) + n(A∩B∩C)