Important Formula: Profit and Loss | Mathematics for RRB NTPC / ASM - RRB NTPC/ASM/CA/TA PDF Download

Profit represents the financial gain when the selling price of an item exceeds its cost price. It is determined by subtracting the cost price from the selling price. On the other hand, a loss occurs when the selling price is lower than the cost price, leading to a financial deficit. The profit formula is expressed as Selling Price − Cost Price, while the loss formula is Cost Price − Selling Price.

What are Profit and Loss?

Profit and Loss are concepts in mathematics that help us determine that the market price of a commodity is sold for a price more than the price at which the commodity is bought or less the price. In mathematics, the profit and loss concept is used to determine the market price of a good and whether or not it is profitable. Every product on the market has a cost price as well as a selling price. Knowing the cost and selling prices of a commodity allows you to calculate the acquired profit or loss.
Profit and Loss are two common terms that are widely used in our daily life, and the meaning of profit and loss are:

• Profit: It is the difference in the money that a person gains when he sells any object. For example, if Kabir buys 12 banans at 24 rupees and sells each banana at 3 rupess he makes a profit of 1 rupees in selling each banana.
• Loss: It is the difference in the money that a person looses when he sells any object. For example, if Kabir buys 12 banans at 24 rupees and sells each banana at 1.5 rupess he makes a loss of 0.5 rupees in selling each banana.

For example, a businessman makes a profit when the selling price of an item is higher than the cost price of that item, and a loss when the cost of purchasing the item is more than the selling price.

Basic Concepts of Profit and Loss

In Profit and Loss, the most basic concepts are the prices of various items throughout the cycle of their purchase and sale. These prices are Cost Price, Selling Price, and Marked Price which are abbreviated as C.P., S.P., and M.P., respectively.

Cost Price (CP)

Cost price (CP) of a product is the amount paid for it. In some cases, it also covers overhead costs, transportation costs, etc.

For example: You bought a refrigerator at Rs 20,000 and spent Rs 4000 for transportation and Rs 1000 for set up. So the total cost price is the sum of all the expenditures done which will be Rs 25000.

Cost Price Formula

Formula for cost price is given as:

Cost Price = Selling Price – Profit
Cost Price = Selling Price + Loss

Selling Price (SP)

The selling price (SP) of a product is the amount at which it is sold. It might be greater, equal to, or less than the product’s cost price.

For example: If a shopkeeper bought a chair at Rs 1500 and sold it at Rs 1900, then the cost price of the chair is Rs 1500 and the selling price of the chair is Rs 1900.

Selling Price Formula

Formula for selling price is given as:

Selling Price = Cost Price + Profit
Selling Price = Cost Price – Loss

Marked Price (MP)

It is the price that is displayed on an item or commodity. It is sometimes referred to as the list price or the tag price. If there is no discount applied to the listed price, the selling price is the same as the marked price.
For example: Suresh goes to a mall for shopping where every product is given a discount offer of 60%. When the price on a stand is written as Rs.150. It implies that the Marked Price of the stand before the discount is Rs. 150.

Marked Price Formula

Formula for Marked price is given as:

Marked Price = Selling Price + Discount

Profit and Loss

Profit and Loss are two major financial concepts which help us understand vast variety of things from daily budgeting to complex economical models. Profit and Loss also help us estimate the market price of a commodity and to assess how profitable a firm is. There is a selling price and a cost price for every product. Based on the values of these prices, we may compute the profit or loss for a certain product.

Profit (P)

Profit is defined as the amount gained by selling a product that is more than the product’s cost price. It is the total amount gained from any business activity.

For example: If a plot was purchased at Rs 150,000 and three years later it was sold at Rs 3,50,000 then there is a profit of 2 lakh.

Loss (L)

When a product is sold for less than its cost price, the seller incurs a loss.

For example: If an I-pad is bought at Rs 30,000 and a year later it was sold for Rs 20,000 then the seller made a loss of Rs 10000.

Profit and Loss Formula

Different formulas for Profit and Loss are discussed in the following:

Profit Formula

Profit is better defined as the difference between the cost price and the selling price. A product’s or commodity’s cost price is its real price, but the selling price is the amount at which the product or commodity is sold. So, if the product’s selling price surpasses its cost price, the corporation has generated a profit. Below is a basic profit formula:

Profit = SP – CP

where,

• CP is Cost Price of Goods
• SP is Selling Price of Goods

Loss Formula

When the cost price of a transaction is greater than the selling price, we incur a loss.
For Example: If a salesperson has bought a textile material for Rs.500 and has to sell it for Rs.350/-, he has incurred a loss of Rs.150/-.

Loss = C.P. – S.P.

Where,

• C.P. is the cost price of the goods, and
• S.P. is the selling price of the goods.

Discount Formula

When the item is sold at a price which is less then the marked price, then we say item is sold at discount and it can be calculated using the formula,

Discount  = M.P. – S.P.

Where,

• M.P. is the marked price of the goods, and
• S.P. is the selling price of the goods.

Profit and Loss Examples

• Mark invests $10,000 in shares of a technology company. Over the year, the value of his investment grows to $12,000, so his profit from this investment would be $12,000 (final value) – $10,000 (initial investment) = $2,000. Conversely, if the market value had dropped and his investment was worth only $9,000 at the end of the year, Mark would face a loss of $10,000 (initial investment) – $9,000 (final value) = $1,000.
• Alex buys a used car for $5,000, intending to sell it for a profit. After purchasing, he spends an additional $500 on repairs and improvements. He then sells the car for $6,200. To find his profit, Alex subtracts his total expenses ($5,500) from his sale price, which is $6,200 – $5,500 = $700.

Profit and Loss – Percentage Formula

Profit and Loss percentage is the profit and loss represented in the form of percentage and the formula for these are discussed as follows:

Profit Percentage

Profit percentage (%) represents the amount of profit as a percentage of the total. Because this profit is proportional to the cost price, the profit Percentage Formula is based on Profit and C.P.
As a result of this, The profit calculation formula will be:

Profit Percent = (Profit × 100)/ C.P.

where C.P. is Cost Price of Goods

Loss Percentage

The loss percentage formula is used to compute the percentage loss in any parameter and as we already know that the difference between the cost price and the selling price is known as the loss. And the percentage loss is the loss as a percentage of the actual cost price.

Loss Percentage = (Loss x 100)/C.P

where C.P. is Cost Price of Goods

Discount Percentage

Discount Percentage change is the discount represented in the percentage form and can be calculated using the following formula:

Discount Percentage = (Discount / M.P.) × 100

Where M.P. is Marked Price of Goods

The aforementioned formulas can also be used as Percent Decrease Formula and Percentage Increase Formula.

Profit and Loss Tricks

There are various points or short tricks that can be remembered to solve the problems of Profit and Loss with ease. Some of such points are as follows:

• Profit (P) = SP – CP If SP > CP
• Loss (L) = CP – SP If CP > SP
• Profit (P%) = (P/CP) × 100
• Loss (L%) = (L/CP) × 100
• Selling Price (SP) = {(100 + P%)/100} × CP
• Selling Price (SP) = {(100 – L%)/100} × CP
• Cost Price (CP) = {100/(100 + P%)} × SP
• Cost Price (CP) = {100/(100 – L%)} × SP
• Discount = Marked Price – Selling Price
• Selling Price = Marked Price – Discount
• When there are two profits, say x% and y%, then the net percentage of profit equals to [x+y+(xy/100)]
• When profit is x%, and loss is y%, then the net % of profit or loss will be: [x-y-(xy/100)]
• If a product is sold at x% profit and then again sold at y% profit then the actual cost price of the product will be CP = [100 x 100 x P/(100+x)(100+y)]. In case of loss, CP = [100 x 100 x L/(100-x)(100-y)]
• If Profit % and Loss % are equal then, P = L and %loss = (Profit)2/100

How to Calculate Profit and Loss?

The cost price and selling price of the goods must be known in order to compute profit and loss. We can use the following steps to calculate the profit and loss for any given data set.

• Step 1: Check whether the cost price is greater than the selling price or the selling price is greater than the cost price.
• Step 2: If the cost price is greater than the selling price, then calculate the Loss using the following formula:
  Loss = Cost Price – Selling Price
• Step 3: If the Selling Price is greater than the cost price, then calculate the profit using the following formula:
  Profit  = Selling Price – Cost Price 

Summarizing Important Formulas – Profit and Loss

• Profit = SP – CP
• Loss = CP – SP
• Profit (%) = {Profit/CP} × 100
• Loss (%) = {Loss/CP} × 100
• Discount = Marked Price – Selling Price
• Discount (%) = (Discount/MP) × 100

Solved Examples

Example 1: A shopkeeper buys juice cans in bulk for Rs 50 each. He sells them for Rs 30 each. Calculate the loss and the loss percentage.
Sol: Given,
Selling price = Rs 30
Cost price = Rs 50
Using loss formula,
Loss = C.P. – S.P.
Loss = 50 – 30 = Rs 20
Using Loss Percentage Formula,
Loss% = (loss/ C.P.) × 100
Loss Percentage = (20 /50) × 100 = 40%
Loss = Rs 20
Loss Percentage = 40%

Example 2: If a vendor sells fruits at Rs.350 per kg, whose cost price is Rs.250/- per kg. What will be the profit gained by the vendor? Find the profit percentage.
Sol: Given, 
Cost Price = Rs.250
Selling Price = Rs.350
Profit = Selling Price – Cost Price
Profit = 350 – 250 = 100
Profit % = (Profit / Cost Price ) × 100
Profit % = (100 /250) × 100
Profit % = 40 %