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Basic Concepts

The basis of commerce is the buying and selling of things. A person buys things and would like to sell them and thereby make a profit on them. The price at which he buys is called the cost price (CP) and the price at which he sells is called the selling price (SP).

The difference between these is profit. So, if one buys a watch for Rs 25 and sells for Rs 30, the profit made is (30-25) = 5. We can thus say that Profit = SP - CP.

Cost Price (CP): The price at which an article is bought, including all costs such as transportation, taxes, etc.

Selling Price (SP): The price at which an article is sold.

Profit or Gain: If SP is greater than the CP, the seller makes a profit or gain. Gain = (SP) - (CP)

Loss: If SP is less than the cost price, the seller makes a loss. Loss = (CP) - (SP)

Basic Formulae:

(i)         Gain = (SP) - (CP)

(ii)        (ii) Loss = (CP) - (SP)

(iii)      (iii) Gain % = [(SP - CP) × 100]/CP).

(iv)      (iv) Loss % = [(CP - SP) × 100]/CP)

If an article is sold at a gain of 20%, then SP = (120% of CP), or 1.2 × CP,
or 6/5 × CP.
If an article is sold at a loss of 20%, then SP = (80% of CP), or 0.8 × CP,
or 4/5 × CP.
Note that the ability to move from fractions to decimals is of prime importance. Sums can be done quickly by using one or the other.


Profit or loss is always calculated on the Cost Price

•  Cost Price (CP): All overhead expenses such as transportation, taxes etc. are also included in the cost price.

  Selling Price (SP): The sum of money, which is finally received for the product.

  Profit: There is gain in a transaction if the selling price is more than the cost price. The excess of the selling price to the cost price is  the profit in the transaction.

Profit = Selling Price - Cost Price

% Profit = 100 × Profit/Cost price

Loss: When the selling price is less than the cost price there is loss in the transaction. The excess of cost price over the selling price is the loss in the transaction.

Loss = Cost Price - Selling Price

% Loss = 100 × Loss/Cost price

Equal % profit & loss on the same selling price of two articles:

If two items are sold each at Rs X, one at a gain of p% and the other at a loss of p%, then the two transactions have resulted in an overall loss of p2/100 %.

Wrong Weight: When a tradesman professes to sell at cost price, but uses a false weight, then the percentage profit earned = (100 × error)/(true weight – error).

Successive Discounts: When a tradesman offers more than one discount to the customer, then sometimes you need to calculate the single discount, which is equal to the two discounts given. There you can apply the method of decimals learned in the concepts of percentages.

Single discount, which is equal to two successive discounts of M% and N% = (M + N – MN)/100)%.

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