\displaystyle \textbf{Cost Price (C.P.)}
\displaystyle \text{The price at which an article is purchased is called its cost price (C.P.).}
\displaystyle \\
\displaystyle \textbf{Overhead Expenses}
\displaystyle \text{Sometimes, in addition to the purchase price of an article, a person may}
\displaystyle \text{have to spend money on transportation, labour charges, repairs, packing,}
\displaystyle \text{installation, etc. Such expenses are called overhead expenses.}
\displaystyle \text{Overhead expenses are included in the actual cost price of the article.}
\displaystyle \text{Thus,}
\displaystyle \text{Actual C.P.}=\text{Purchase Price}+\text{Overhead Expenses}.
\displaystyle \\
\displaystyle \textbf{Selling Price (S.P.)}
\displaystyle \text{The price at which an article is sold is called its selling price (S.P.).}
\displaystyle \\
\displaystyle \textbf{Gain or Profit}
\displaystyle \text{If S.P.}>\text{C.P., the seller makes a gain or profit.}
\displaystyle \text{Gain}=\text{S.P.}-\text{C.P.}
\displaystyle \\
\displaystyle \textbf{Loss}
\displaystyle \text{If S.P.}<\text{C.P., the seller incurs a loss.}
\displaystyle \text{Loss}=\text{C.P.}-\text{S.P.}
\displaystyle \\
\displaystyle \textbf{Important Note}
\displaystyle \text{Gain or loss percentage is always calculated on the cost price (C.P.).}
\displaystyle \\
\displaystyle \textbf{Gain and Loss Percentage}
\displaystyle \text{Gain }\%=\frac{\text{Gain}}{\text{C.P.}}\times100.
\displaystyle \text{Loss }\%=\frac{\text{Loss}}{\text{C.P.}}\times100.
\displaystyle \\
\displaystyle \textbf{To Find S.P. When C.P. and Gain or Loss Percentage are Given}
\displaystyle \text{(i) If C.P. and gain }\%\text{ are given, then}
\displaystyle \text{S.P.} =\frac{100+\text{Gain }\%}{100}\times\text{C.P.}
\displaystyle \text{or}\qquad \text{S.P.}=\left(1+\frac{\text{Gain }\%}{100}\right)\text{C.P.}
\displaystyle \text{(ii) If C.P. and loss }\%\text{ are given, then}
\displaystyle \text{S.P.} =\frac{100-\text{Loss }\%}{100}\times\text{C.P.}
\displaystyle \text{or}\qquad \text{S.P.}=\left(1-\frac{\text{Loss }\%}{100}\right)\text{C.P.}
\displaystyle \\
\displaystyle \textbf{To Find C.P. When S.P. and Gain or Loss Percentage are Given}
\displaystyle \text{(i) If S.P. and gain }\%\text{ are given, then}
\displaystyle \text{C.P.} =\frac{100}{100+\text{Gain }\%}\times\text{S.P.}
\displaystyle \text{(ii) If S.P. and loss }\%\text{ are given, then}
\displaystyle \text{C.P.} =\frac{100}{100-\text{Loss }\%}\times\text{S.P.}
\displaystyle \\
\displaystyle \textbf{Marked Price (M.P.)}
\displaystyle \text{The price marked or printed on an article is called its marked price (M.P.).}
\displaystyle \text{A shopkeeper may sell the article at the marked price or offer a discount}
\displaystyle \text{on it.}
\displaystyle \\
\displaystyle \textbf{List Price}
\displaystyle \text{The price of an article quoted in a manufacturer's or seller's price list}
\displaystyle \text{is called its list price. It is generally treated in the same way as the}
\displaystyle \text{marked price when calculating a discount.}
\displaystyle \\
\displaystyle \textbf{Discount}
\displaystyle \text{To promote sales or clear stock, a shopkeeper may reduce the marked price}
\displaystyle \text{of an article. This reduction in price is called a discount.}
\displaystyle \text{Discount}=\text{M.P.}-\text{S.P.}
\displaystyle \\
\displaystyle \textbf{Discount Percentage}
\displaystyle \text{Discount is always calculated on the marked price or list price.}
\displaystyle \text{Discount }\% =\frac{\text{Discount}}{\text{M.P.}}\times100.
\displaystyle \\
\displaystyle \textbf{Selling Price After Discount}
\displaystyle \text{If }d\%\text{ is the rate of discount, then}
\displaystyle \text{S.P.} =\text{M.P.}-\text{Discount}.
\displaystyle \text{Discount}=\frac{d}{100}\times\text{M.P.}
\displaystyle \therefore\ \text{S.P.} =\left(1-\frac{d}{100}\right)\text{M.P.}
\displaystyle \text{or}\qquad \text{S.P.}=\frac{100-d}{100}\times\text{M.P.}
\displaystyle \\
\displaystyle \textbf{Successive Discounts}
\displaystyle \text{If }d_1\%\text{ and }d_2\%\text{ are two successive discounts, the second}
\displaystyle \text{discount is calculated on the price obtained after the first discount.}
\displaystyle \text{S.P.} =\left(1-\frac{d_1}{100}\right) \left(1-\frac{d_2}{100}\right)\text{M.P.}
\displaystyle \\
\displaystyle \textbf{Equivalent Discount for Two Successive Discounts}
\displaystyle \text{If }d_1\%\text{ and }d_2\%\text{ are two successive discounts, then the}
\displaystyle \text{equivalent single discount is}
\displaystyle \left(d_1+d_2-\frac{d_1d_2}{100}\right)\%.
\displaystyle \\
\displaystyle \textbf{Important Points to Remember}
\displaystyle \text{(i) Gain or loss percentage is calculated on C.P.}
\displaystyle \text{(ii) Discount percentage is calculated on M.P. or list price.}
\displaystyle \text{(iii) Discount and loss are not the same. Discount compares M.P. with S.P.,}
\displaystyle \text{whereas loss compares C.P. with S.P.}
\displaystyle \text{(iv) An article sold at a discount can still result in a profit if S.P.}> \text{C.P.}
\displaystyle \text{(v) Successive discounts should not normally be added directly.}
\displaystyle \\

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