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. |

Fixed costs are the expenses which do not vary during the month whereas, variable costs vary.

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

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

### 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:**

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:**

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:**

Loss = 8%

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

= $\frac{100 - 8}{100}$ x 650

= 598