# Profit and Loss

Profit and loss depends on the cost price and selling price of an article.

Suppose, if a person buys an article for $70 and sells it for$100.

The cost-price (C.P.) of an article is the price at which the article is bought = $70 The selling-price (S.P.) of an article is the price at which the article is sold =$100

Since, the selling price of the article is more than its cost price; it is sold at a profit.

and, profit (gain) = $100 -$70 = $30 Thus, profit (gain) = selling price - cost price i.e. profit (gain) = S.P. - C.P. Similarly, if a person buys an article for$100 and sells it for $90; The cost-price of the article =$100

and its selling price = $90 Since, the selling price of the article is less than the cost price; it is sold at a loss. and, loss =$100 - $90 =$10

Thus, loss = cost price - selling price

i.e. loss = C.P. - S.P.

Note: S.P. is the short form for selling price and C.P. is the short form for cost price.

Corollary:

1. When selling price is more than cost price, there is a profit.

(i) profit = selling price - cost price            i.e. profit = S.P. - C.P.

(ii) selling price = cost price + profit          i.e. S.P. = C.P. + profit

(iii) cost price = selling price - profit          i.e. C.P. = S.P. - profit

2. When selling price is less than cost price, there is a loss.

(i) loss = cost price - selling price                i.e. loss = C.P. - S.P.

(ii) selling price = cost price - loss               i.e. S.P. = C.P. - loss

(iii) cost price = selling price + loss             i.e. C.P. = S.P. + loss

Solved examples on profit and loss:

1. A man bought an article for $10.50 and sold it for$12.

Here the cost price (C.P.) of the article is $10.50 and the selling price (S.P.) of the article is$12.00. Since the selling price of an article is more than its cost price; it is sold at a profit (gain).

Profit = selling price (S.P.) - cost price (C.P.)

= $12.00 -$10.50

= $1.50 2. A boy bought a second hand bicycle for$570. After one year he sold it for $350. Here the cost price (C.P.) of the bicycle is$570 and the selling price (S.P.) of the bicycle is $350. Since the selling price of an article is less than its cost price; it is sold at a loss. Loss = cost price (C.P.) - selling price (S.P.) =$570 - $350 =$220

To find Profit or Loss when Cost Price and Selling Price are Given

To find Selling Price when Cost Price and Profit or Loss are Given

To find Cost Price when Selling Price and Profit or Loss are Given

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