# Profit and loss percentage

## Cost Price

While purchasing a good, the amount paid by the shopkeeper is called the cost price of the product. It is represented by CP. It has two types:

• Fixed cost price: this price does not change under any circumstances that may happen
• Variable cost price: this price may change due to the influence of certain situations

## Selling price

While purchasing an item, the amount paid by the customer to the shopkeeper is called the selling price of that product. It is denoted by SP and sometimes is called the sale price of the product.

## Marked price

The price offered by the shopkeeper to the customer before giving a specific discount on the product is called the marked price of that product, represented by MP.
Discount = Marked price – selling price
Discount percentage = (discount / marked price) x 100

## Profit

The amount gained by the shopkeeper after selling a product with a selling price higher than its cost price is called the profit earned by the shopkeeper. It is denoted by P.
Profit (P) = Selling price (SP) – Cost price (CP)

## Loss

The amount lost by the shopkeeper after selling a product with a selling price lower than its cost price is called the loss earned by the shopkeeper. L denotes it.
Loss (L) = Cost price (CP) – Selling price (SP).

## Profit percentage

The percentage the shopkeeper gains after selling a product with a selling price higher than its cost price is the profit percentage of that product. P% denotes it.
Profit Percentage P% = {(selling price – cost price) / cost price} x 100
= (net profit / cost price) x 100

## Loss percentage

The percentage of the amount lost by the shopkeeper after selling a product with a selling price lower than its cost price is called the loss percentage of that product. L% denotes it.
Loss Percentage P% = {(cost price - selling price) / cost price} x 100
= (net loss / cost price) x 100

## Profit and loss tricks

• Profit, P = SP – CP; such that SP>CP
• Loss, L = CP – SP; such that CP>SP
• P% = (P / CP) x 100
• L% = (L / CP) x 100
• SP = {(100 + P%)/100} x CP
• SP = {(100 – L%)/100} x CP
• CP = {100 / (100 + P%)} x SP
• CP = {100 / (100 – L%)} x SP
• Discount = MP – SP
• SP = MP – Discount

Example 1: A stationery merchant bought 35 registers, each for ₹ 280. He sold each of them for ₹ 308. Find his percentage profit.
Solution:
The profit percentage remains the same for one unit as well for all the units. The calculations can be done for one unit and applied to the rest of the units.
CP = ₹ 280
SP = ₹ 308
Profit = 308 – 280 = ₹ 28
Now, apply the profit percentage formula for the same.
Profit percentage = 100 × 28/280 = 10%

Example 2: A piece of furniture is sold for Rs 2400, making a solid profit of 25 %. Calculate the actual profit or loss if it had been sold at Rs 1800?
Solution:
Firstly, find the cost price of the same.
C.P. = 2400 × 100/125 = 1920.
New selling price = ₹ 1800
⇒ Loss = 1920 – 1800 = 120
∴ Loss percentage = 100 × 120/1920 = 6.25%.

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