#### definition

**Cost Price(C.P.):**The buying price of any item is known as its cost price.**Selling Price(S.P):**The price at which you sell any item is known as the selling price.**Total cost price:**In trading, all expenses incurred on an article before it can be sold have to be added to the cost price of the article. That is called the total cost price of the article.**Profit:**Profit is the revenue remaining after all costs are paid from the selling price.**Loss:**When the item is sold and the selling price is less than the cost price, then it is said, the seller has incurred a loss.-
**Overhead expenses:**Additional expenses made after buying an article are included in the cost price and are known as overhead expenses.

#### formula

- Profit = Selling Price - Cost Price, which means CP < SP.
- Loss = Cost Price - Selling Price, which means CP > SP.
- CP = Buying price + Overhead expenses

#### notes

**Concepts of Cost Price, Selling Price, Profit, and Loss:**

**Cost Price(C.P.): **The buying price of any item is known as its cost price. It is written in short as CP.

**Selling Price(S.P):** The price at which you sell any item is known as the selling price. It is written in short as SP.

**Total cost price:** In trading, all expenses incurred on an article before it can be sold have to be added to the cost price of the article. That is called the total cost price of the article.

**Profit: **Profit is the revenue remaining after all costs are paid from selling price.

**Loss: **When the item is sold and the selling price is less than the cost price, then it is said, the seller has incurred a loss.

You can decide whether the sale was profitable or not depending on the CP and SP.

- If CP < SP then you made a profit = SP – CP.
- If CP = SP then you are in a no-profit no loss situation.
- If CP > SP then you have a loss = CP – SP.

**Overhead expenses:**Additional expenses made after buying an article are included in the cost price and are known as overhead expenses.

#### Example

Hamidbhai bought bananas worth 2000 rupees and sold them all for 1890 rupees. Did he make a profit or a loss? How much was it?

He bought bananas for Rs. 2000.

Hence, Cost price = Rs. 2000

Selling price = Rs. 1890

Cost price is greater than selling price. Therefore, Hamidbhai suffered a loss.

Loss = Cost price - Selling price

= 2000 - 1890

= Rs. 110

∴ Hamidbhai suffered a loss of Rs. 110 in this transaction.

#### Example

Harbhajan Singh bought 500 kg of rice for 22000 rupees and sold it all at the rate of Rs. 48 per kg. How much profit did he make?

The cost price of 500 kg rice is Rs. 22000.

Selling price of 500 kg of rice is = 500 × 48 = Rs. 24000

Selling price is greater than cost price.

Therefore, there is a profit.

Profit = Selling price - Cost price

= 24000 - 22000

= Rs. 2000

∴ In this transaction, Harbhajan Singh made a profit of Rs. 2000.

#### Example

Javedbhai bought 35 electric mixers for Rs. 4300 each. To transport them to the shop, he spent Rs. 2100. If he expects to make a profit of Rs. 21000, at what price should he sell each mixer?

Cost price of one mixer Rs. 4300.

Hence cost price of 35 mixers = 4300 × 35 = Rs. 150500

Total cost price = cost of mixers + cost of transport

= 150500 + 2100

= Rs. 152600

Javedbhai wants a profit of 21000 rupees.

∴ Hence, amount expected on selling = 152600 + 21000 = Rs. 173600

Selling price of 35 mixers = Rs. 173600

∴ Selling price of one mixer = 173600 ÷ 35 = Rs. 4960

Javedbhai should sell every mixer for Rs. 4960.

#### Example

The cost of a flower vase is Rs. 120. If the shopkeeper sells it at a loss of 10%, find the price at which it is sold.

**Given:** CP = Rs. 120 and Loss percent = 10.

Loss of 10% means if CP is Rs. 100, Loss is Rs. 10

Therefore,

SP would be Rs.(100 - 10) = Rs. 90

When CP is Rs. 100, SP is Rs. 90.

Therefore, if CP were Rs. 120 then

SP = `90/100 xx 120` = Rs. 108.

**Given:** CP = Rs. 120 and Loss percent = 10.

Loss is 10% of the cost price

= 10% of Rs. 120

= `10/100 xx 120`

= Rs. 12

Therefore,

SP = CP - Loss = Rs. 120 - Rs. 12 = Rs. 108

#### Example

Selling price of a toy car is Rs. 540. If the profit made by the shopkeeper is 20%, what is the cost price of this toy?

**Given:** SP = Rs. 540 and the Profit = 20%.

20% profit will mean if CP is Rs. 100, profit is Rs. 20.

Therefore, SP = 100 + 20 = 120

Now, when SP is Rs. 120, then CP is Rs. 100.

Therefore, when SP is Rs. 540,

Then CP = `100/120 xx 540` = Rs. 450.

**Given:** SP = Rs. 540 and the Profit = 20%.

Profit = 20% of CP and SP = CP + Profit

So, 540 = CP + 20% of CP

= CP + `20/100 xx "CP" = [1 + 1/5]"CP"`

= `6/5 "CP"`.

Therefore, `540 xx 5/6` = CP or Rs. 450 = CP

#### Example

Meenu bought two fans for ₹ 1200 each. She sold one at a loss of 5% and the other at a profit of 10%. Find the selling price of each. Also, find out the total profit or loss.