Cost Price (C.P.): The price, at which an article is purchased, is called its cost price.

Overhead Expenses: Sometimes apart from paying the cost of an article, a person has to spend money on its transportation (cartage), labor charges, repair, sales tax, etc. Such expenses are known as overhead expenses.

Overhead Expenses are always included in the C.P. of the article. Thus, we have $\text{ Actual C.P. of the article = Cost of the article + Overhead expenses }$

Selling Price (S.P.): The price, at which an article is sold, is called its selling price.

Gain and Loss:

a) If $\text{S.P.} > \text{C.P.}$, then the seller has a gain or a profit. $\text{Gain = S.P. - C.P.}$

b) If $\text{S.P.} < \text{C.P.}$, then the seller has a loss. $\text{Loss = C.P. - S.P.}$

Note: Loss or Gain is always reckoned on C.P.

Gain and Loss Percent Formula: $\displaystyle \text{i) } Gain \ \% = \Big( \frac{Gain}{C.P.} \times 100 \Big) \%$ $\displaystyle \text{ii) } Loss \ \% = \Big( \frac{Loss}{C.P.} \times 100 \Big) \%$

To find $S.P$ when $C.P$ and gain or loss percent are given

i) When $C.P.$ and $gain\%$ are given, then $\displaystyle S.P. = \frac{(100+ Gain\%)}{100} \times C.P.$

ii) When $C.P.$ and $loss\%$ are given, then $\displaystyle S.P. = \frac{(100 - Loss\%)}{100} \times C.P.$

To find C.P., when S.P. and gain or loss per cent are given

i) When $S.P.$ and $gain\%$ are given, then $\displaystyle C.P. = \frac{100}{(100 + gain\%)} \times S.P.$

i) When $S.P.$ and $loss\%$ are given, then $\displaystyle C.P. = \frac{100}{(100 - loss\%)} \times S.P.$

Discount

Marked Price: The price that is marked on the article in shops called the Marked Price of that article, abbreviated as M.P.

List Price: Items which are manufactured (or packed) in a factory are marked with a price according to the list supplied by the factory, at which the retailer is supposed to sell them. This price is known as the list price of the article.

Discounts: In order to give a boost to the sale of an item or to clear the old stock, sometimes the shopkeepers offer a certain percentage of rebate on the marked price. This rebate is known as discount.

Note: Discount is always calculated on the marked or list price. Thus, by a discount of 10%, we mean that the customer can get the article at a price obtained by reducing its marked price by 10%. $\displaystyle \text{Selling Price (S.P.) = Marked Price (M.P.) - Discount}$ $\displaystyle S.P. = \Big( 1 - \frac{d}{100} \Big) \times M.P.$

If $d \%$ is the rate of discount, then Successive Discounts: If $d_1\%$ and $d_2\%$ are two successive discounts, then $\displaystyle S.P. = \Big( 1 - \frac{d_1}{100} \Big) \Big( 1 - \frac{d_2}{100} \Big) \times M.P.$