Profit and Loss

In Maths, we have learned about the terms numbers, equations, functions etc. which are commonly used to solve mathematical problems. Profit and loss are also the mathematical terms which are used to calculate many problems in our daily life. Just like other mathematical formulas, such as algebra, we have formulas to calculate profit and loss too.

Basically, profit and loss concepts are applicable to determine the price of a commodity in the market. Every product has a cost price and selling price. Based on the values of these prices, we can calculate the profit gained and also the loss of money in a particular product. For a shopkeeper, if the value of selling price is more than the cost price of a commodity, then its a profit to him and vice-versa will be a loss for him.

Here, in this article, we will discuss profit and loss maths along with tricks to solve profit and loss problems.

Profit and Loss in Maths

Let us learn profit and loss concepts according to mathematics. It is better explained in terms of cost price and selling price. We will also learn the concepts with the help of profit and loss examples.

Cost Price: The amount paid for a product or commodity to purchase it, is called a cost price. Also, denoted as CP. This cost price is further classified into three different categories:

  • Fixed Cost: The fixed cost is constant, it doesn’t vary under any circumstances
  • Variable Cost: It could vary depending as per the number of units

Selling Price: The amount for which the product is sold is called Selling Price. It is usually denoted as SP.

Marked Price: This is basically labeled by Shopkeepers to offer a discount to the customers in such a way that,

Discount = Marked Price – Selling Price

And Discount Percentage = (Discount/Marked price) x 100

Profit(P): The amount gained after selling a product more than its cost price.

Loss(L): The amount, the seller gets after selling the product less than its cost price, is mentioned as a loss.

Profit and Loss Formulas:

Now let us define profit formula and loss formula;

Profit or Gain = Selling price – Cost Price

Loss = Cost Price – Selling Price

In terms of percentage;

Profit percentage = (Profit /Cost Price) x 100

Loss percentage = (Loss / Cost price) x 100

Let us explain above given formulas with profit and loss examples;

Example: Suppose a shopkeeper has bought 1 kg of apples for 100 rs. And sold it for 120 kg. How much is the profit he got?

Cost Price for apple is 100 rs.

Selling Price for apple is 120 rs.

Then profit gained by shopkeeper is ; P = SP – CP

P = 120 – 100 = 20 rs.

Example: For the above example calculate the percentage of the profit gained by the shopkeeper.

We know, Profit percentage = (Profit /Cost Price) x 100

Therefore, Profit percentage = (20/100) x 100 = 20%.

Points to remember:

  • For profit, the selling price should be more than the cost price
  • For loss, cost price should be more than the selling price.
  • The percentage value for profit and loss is calculated in terms of cost price.

Profit and Loss Tricks

As you have learned until now how to calculate profit and loss and also the percentage of them. Now let us learn some tricks or formulas to solve profit and loss problems, starting from the general formulas.

  1. Profit, P = SP – CP; SP>CP
  2. Loss, L = CP – SP; CP>SP
  3. P% = (P/CP) x 100
  4. L% = (L/CP) x 100
  5. SP = {(100 + P)/100} x CP
  6. SP = {(100 – L)/100} x CP
  7. CP = {100/(100 + P)} x SP
  8. CP = {100/(100 – L)} x SP
  9. Discount = MP – SP
  10. SP = MP -Discount
  11. For false weight, profit percentage will beP% = (True weight – false weight/ false weight) x 100.
  12. When there are two successful profits say m% and n%, then the net percentage profit equals to: (m+n+mn)/100
  13. When the profit is m% and loss is n%, then the net % profit or loss will be: (m-n-mn)/100
  14. If a product is sold at m% profit and then again sold at n% profit then the actual cost price of the product will be:CP = [100 x 100 x P/(100+m)(100+n)]

    In case of loss,

    CP = [100 x 100 x P/(100-m)(100-n)]

  15. If P% and L% are equal then, P=LAnd %loss = P2/100

Problem: A man buys a fan for Rs. 1000 and sells it at a loss of 10%. What is the selling price of the fan?

Solution: Cost Price of the fan is Rs.1500

Loss percentage is 15%

As we know, Loss percentage = (Loss/Cost Price) x 100

15 = (Loss/1000) x 100

Therefore, Loss = 150 rs.

Since, Loss = Cost Price – Selling Price

Selling Price = Cost Price – Loss

= 1000 – 150

Selling Price = R.850/-

Problem: If a pen cost Rs.50 after 10% discount. Then what is the actual price or marked price for Pen?

Solution: MP x (100 – 10) /100 = 50

MP x 90/100 = 50

MP = 50 x 100/90

MP = Rs. 55.55

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Practise This Question

Solve the following pair of linear equations:
2x+3y=2
4x9y=1
(where x>0,y>0)