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# Profit and Loss

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 Sub Topics When we buy a thing by paying some money and sell it back, then definitely we will be in either profit or loss. This profit and loss depends on selling and cost price. The 'cost price' is that cost which is paid for purchasing an item and selling price is that price which is taken for item in case of selling it. Profit and loss is very useful in our daily life. Profit and loss can be seen very useful in field of business, finance and other transactions in our day to day life. It includes what % of total profit or total loss is gained. Both profit % and loss % are calculated on behalf of cost price.Profit and Loss Definition can be given as follows: When selling price is more than that of cost price, then it is called profit. Formally, it can be given as Profit = selling price - cost price. When cost price is more than selling price, then it will be known as loss and it can be given as Loss = cost price - selling price. Let us see some Profit and Loss Problems to see that how Profit and Loss depends on selling and cost price. Suppose a shopkeeper purchases scientific watches paying $\$$20 each. If selling price for each of them is \$$ 50, then it is clear that cost price of each watch is$\$$20 and selling price is \$$50.Profit = selling price (s. p.) - cost price (c. p.), = $\$$50 - \$$20, =$\$$25.If shopkeeper sells watches for \$$10 each and cost price is same for each watch that is $\$$20, then there will be loss and it can be shown as: Loss = cost price (c. p.) – selling price (s. p.). = \$$20 -$\$$10 = \$$10.

## Cost Price

If a product is offered to satisfy a demand, our first concern is to know the cost of product, known as cost price. Items that are bought and sold have a cost to the seller and a price to the buyer. The price at which an article is purchased is called the cost price. It is the set of the costs involved to offer a product, whether this product is a good or a service. Before calculating the cost price, we need to know about the fixed costs and variable costs.
Fixed costs are the expenses which do not vary during the month whereas, variable costs vary.

## Selling Price

The price at which an article is sold is called the selling price. Also known as the retail price, it is the amount you sell the goods for a seller who is willing to accept

## Profit and Loss Formula

Given below are the formula's of profit and loss.

Profit = Selling Price - Cost Price

Profit percentage = [$\frac{\text{profit}}{\text{cost price}}$ x 100]

Selling price = [$\frac{\text{100 + profit percent}}{100}$] x cost price

Loss = Cost Price - Selling Price

Loss percentage = ($\frac{\text{loss}}{\text{cost price}}$ x 100)

Cost price = [$\frac{\text{100 - loss percent}}{100}$] x cost price

Profit % or loss % is always calculated on the cost price.
If a trader professes to cell his goods at cost price but uses false weight, then

Profit % = [$\frac{\text{Error}}{\text{true value - error}}$ x 100]%

### Solved Examples

Question 1: The table is brought for $\$$1950 & sold at \$$2340. Find the profit per cent. Solution: Cost price =$\$$1950 and selling price = \$$2340

Profit = [$\$$2340 - \$$1950] =$\$$390 Profit % = [\frac{\text{profit}}{\text{cost price}} x 100 ] % = (\frac{390}{1950} x 100)% = 20% Question 2: Apples are bought at 80 a dozen and sold at a profit of 5%. Find the selling price of each apple. Solution: Cost price = \$$80 & profit% = 5%

Selling price = [$\frac{\text{100 + profit%}}{100}$] x cost price

= ($\frac{100 + 5} {100}$) x 80

= 84
Hence, selling price of each apple = $\frac{84}{12}$ = 7

## Profit and Loss Examples

Given below are some of the examples on profit and loss.

### Solved Examples

Question 1: A man sold two cows for 25500 each on one he gains 20% and on the other he losses 20%. Find his gain or loss percent in the whole transaction.
Solution:
Selling price of the first cow = 25500
Profit percent = 20%

Cost price of the first cows = $\frac{25500 \times 100}{120}$

= 21250

Selling price of the second cow = 25500
Loss percent = 20%

Cost price of the second cow = $\frac{25500 \times 100}{80}$

= 31875
Total cost price of both the cows = (21250 + 31875)
= 53125
Selling price = (2 x 25500) = 51000
Loss = Selling Price - Cost Price
= 53125 - 51000
= 2125

Loss Percent = ($\frac{2125}{53125}$ x 100 )%

= 4%

Question 2: A watch is bought for 780 and sold at 650. Find the loss percent?
Solution:
Cost Price = 780
Selling Price = 650
Loss = Cost price - Selling price
= (780 - 650) = 130

Loss Percent = ( $\frac{\text{Loss}}{\text{Cost price}}$ x 100 ) %

= ($\frac{130}{780}$ x 100 )%

= 16 ($\frac{2}{3}$ ) %

Question 3: Chair is brought for 650 and sold at a loss of 8%. Find its selling price.
Solution:
Cost Price = 650
Loss = 8%

Selling price = $\frac{\text{100 - Loss%}}{100}$ x Cost Price

= $\frac{100 - 8}{100}$ x 650

= 598