Commercial Arithmetic

Profit and loss:


The money paid to buy goods is called cost price and abbreviated as C.P. The price at which goods are sold in shops is called selling price and abbreviated as S.P.

When an article is bought, some addition expenses such as freight charges, labour charges, transportation charges, maintenance charges etc., are made before selling. These expenses are known as overhead expenses. These expenses have to be included in the cost price. Thus,


Real cost price = total investment

⇒ C.P. = price for + overhead


Buying goods charges

  • If S.P > C.P., there is a gain or profit.
  • If S.P > C.P., there is a loss.
  • Profit = S.P – C.P.
  • Loss = C.P – S.P.
  • Gain (profit) or loss on 100 is called gain percent or loss percent.


Profit or Loss is always calculated on C.P

  1. Gain or profit % = Gain/P ×100
  2. Loss % = Loss/P×100
  3. P.= (100+Gain%)/100× C.P
  4. P. = (100-Loss%)/100 x C.P
  5. P.= 100/(100+gain%) × S.P
  6. P = 100/(100-LOSS%)×S.P


A reduction on the market price of articles is called discount. The following completely describe facts related to the discount:

  • Discount is always given on the marked price of the article.
  • Discount =Marked price – Selling price.
  • Marked price is called list price.
  • Discount = Rate of discount × Marked price
  • Net price [S.p] = Marked price – discount.


The mediator who helps buying and selling of houses, sites, vehicles etc., is called commission agent or broker.

The money that the broker or agent receives in the deal is called brokerage or commission.

Commission is calculated on the transaction amount in percentage.

Commission per hundred rupees is called commission rate.

Commission = Commission rate ×S.P

Selling price = 100/commission rate   ×𝑐𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛.

Simple Interest


People borrow money from banks or financial institutions or money lenders for various purposes. While returning the borrowed money after a period of time, they need to pay some extra amount. This extra amount paid on the borrowed money after a period of time is called interest.

Principal : The money borrowed is called principal or sum.

Interest : The extra money paid on the principal after a period of time is called interest.

Amount : The total money paid is called amount.  Amount = Principal + Interest.

Rate : Interest for every Rs 100 for one year is known as rate percent per annum.

Time : Time is the duration for which the borrowed money is utilised. Time is expressed in years or months or days.

Simple interest : The interest paid on the principal alone. In the world of finance (Bankers rule), time is often expressed in days also.


Formula to find the simple interest

Let P = principal,

R = rate of interest per annum,

T = time in years,

I = simple interest. These are related by the formula.

I = (PxTxR)/100  

When the time is given in days or months, it is be expressed in years.

For calculating interest, the day on which money deposited is not counted, while the day on which money is withdrawn is counted.


The Government requires money for its functioning. Money required for a Government is collected from the public in the form of taxes. One such method of collecting money is sales tax.

Value added tax (VAT): VAT is revised version of sales tax.


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