[Maths Class Notes] on Profit Pdf for Exam

Profit Formula

When the cost price is subtracted from the selling price, the resulting answer is the profit. 

Profit = Selling Price – Cost Price

P = SP – CP

If the answer to SP – CP comes as a positive integer, then we have a profit. If it is a negative integer, we have a negative profit, which is termed as a loss. 

Profit Percentage

A percentage is one of the most preferred ways of comparing two quantities. The profit is always compared to the cost price unless it is explicitly mentioned in the question that it is compared to the selling price. Suppose Leela has a 20% profit percentage. Then, she has earned Rs.20 profit for every Rs.100 at cost price. 

Profit Percentage = [(frac{text{Profit}}{text{Cost Price})}] × 100

P% = [(frac{P}{CP})] × 100

Difference Between Profit and Gain

Types of Profit

The three main types of profit are explained below:

1. Gross Profit: Gross profit is the profit that a company makes after subtracting the costs of manufacturing and selling its products.  Also called gross income, it is calculated by subtracting the cost of goods sold from revenue. The gross profit contains only variable costs and does not contain fixed costs.

2. Operating Profit: Operating profit represents the additional income that remains after accounting for all the costs of doing business. It is basically the ratio of the operating income to the sales revenue. 

Operating Profit = Operating Income: Sales Revenue

3. Net Profit: Net profit is the money that remains after accounting for every sing expense or cost incurred by the company. It is the most important thing to ensure the company’s financial health. 

Solved Problems

Example 1: A retailer bought 10 apples for Rs. 100. He sold them for Rs. 150. How much is the profit he got per apple? What is his total profit?

Solution:

Cost Price (10 apples) = Rs.100

Cost Price (1 apples) = 100/10 = Rs. 10

Selling Price (10 apples) = Rs. 120 

Selling Price (1 apples) = 120/10=Rs.12

Profit (for 1 apple) = SP-CP (one apple)

 = 12 – 10= Rs. 2

So, his profit per apple is Rs. 2.

Profit (10 apples) = SP-CP (ten apples)

= 120 – 100= Rs. 20

So, his total profit is Rs. 20.

Example 2: A girl buys a blue umbrella for Rs. 200 and sells it at a profit of 25%. What is the selling price of the fan?

Solution: 

Cost Price (umbrella) = Rs.200

Profit Percentage = 25%

P% = (P/CP) × 100 

25 = (P/200) x 100

P = Rs. 50

As we know,

P = SP-CP

SP = CP+P

SP = 200 + 50

Selling Price = Rs. 250 

Therefore, the selling price of the umbrella was Rs. 250. 

Example 3: Meera sold a beautiful sculpture for Rs.5,000, on which she makes a profit of 25%. What is the amount of money she spent while making the sculpture?

Solution: 

Profit Percentage = 25%

Selling Price= Rs. 5000

CP + (25/100 of CP) = 5000

(125/100) * CP = 5000

(5/4) * CP= 5000

CP= 5000* (4/5)

CP=Rs. 4000

Therefore, the cost price of the sculpture is Rs. 4000.