**What is profit And loss?**

Let's start with an example to understand about 'Profit and Loss'. For instance, we went to the watch shop. One watch is so good and you liked it. After seeing the price tag you are just shocked. The price mentioned on the Watch is Rs. 2500. You want a discount on it, you went to the shopkeeper and asked for a discount. He offers you a discount of 20%. So now what is the final amount you need to pay for shopkeeper?

Did you say Rs 2000/-? Great, that is right. You will pay the amount after subtracting 20% of the amount on price tag i.e. Rs. 500/- from Rs. 2500/-. You finally pay him Rs2500 – Rs500 = Rs. 2000. This is one example of the concept of discount and marked price. What you learned here from this example is, the discount is calculated on the marked price. Now let’s think that the shopkeeper has purchased the watch for Rs. 1600/-. What do you think the money the shopkeeper made by selling the Watch? We know the shopkeeper has invested Rs. 1600/- to buy this watch and he/she sells for Rs. 2000/-. He/she makes a profit of Rs. 2000 – Rs 1600 = Rs. 400/-. He/she earns all the profit by investing Rs. 1600 from his pocket and makes a profit of 400 on his cost price of Rs. 1600. Hence his percentage of profit is 100 × 400/1600 = 25%. This is the concept of the cost price and profit. The amount you put in, to buy any product is called cost price and the additional amount you get after selling the product is known as profit. Now let’s check on the profit and loss percentage. Profit and Loss percentage are calculated on the cost price. These Profit and loss questions are an integral part of all many competitive exams. We need to understand all the basic terms used in profit and loss problems.

**Cost Price (CP):**The amount invested to acquire a product, is called ‘cost price’. All the other expenses like packing, transportation, and inventory are included in the Cost Price(CP).**Selling Price (SP):**The amount with which the product is sold is called ’selling price’. The price at which the product is sold after any discounts is called the Selling price.**Marked Price (MP):**The price/amount the product is tagged for selling is also known as ‘marked price’. Sometimes it is also called a printed price /quotation price/catalog price/invoice price.**Profit:**If the selling price is more than the Cost price, then the difference between SP and CP is called Profit or gain.

PROFIT = SELLING PRICE (SP) – COST PRICE(CP)

Example: Let the cost price of a kg of rice be Rs 50/- and the shopkeeper sells the same for Rs 55/- per kg, then profit = Rs 55 – Rs 50 = Rs. 5 per kg**Loss:**When the selling price is less than the Cost price, then the difference between CP and SP is called Loss.

LOSS = COST PRICE (CP) – SELLING PRICE (SP)

E.g. Let the cost price of a dozen bananas is Rs. 60/-. If the fruit vendor sells each banana for Rs. 4, then selling price for dozen bananas = Rs. 12*4 = Rs. 48/-

Selling price = Rs. 4 / banana ∴ Loss = Rs. 5 – Rs. 4 = Re. 1 per banana.

**Note**: Profit or loss percentage is calculated on the cost price unless otherwise specified. Now let’s check profit or loss formula in percentage, followed by questions on profit and loss.**Profit percentage formula:**

Profit percentage (Profit %) = 100 × Profit/Cost Price.**Percentage Loss:**

Loss percentage (Loss % ) = 100 × Loss/Cost Price.

## Profit and Loss Formulas and Rules:

Profit and Loss are integral parts of many competitive exams. It is sometimes better if you can remember the following formulas on profit and loss to solve problems on them. Below are some important formulas for solving Profit and loss questions.

**Equal % profit & loss on the identical selling price of 2 articles:**

If two articles are sold at Rs X each, one at a loss percentage of p and the other at a gain percentage of p, then the two transactions resulted in a loss of (p2/100) %. This is the loss percentage.

The absolute value of the loss is calculated with = Rs (2.p2.X)/(1002-p2)**Equal % profit & loss on the identical cost price of 2 articles:**

If the cost price of two articles is X, and one is sold at a loss percentage of p and the other at a profit percentage of p, then there is no loss or no gain on the two transactions.**Trade Discount:**

It is a very common practice to announce some discount on the marked/tagged price of an article to attract customers.

Note: The discount is always given as % of the marked price unless specified. For example. Suppose the list price of an item is Rs. 450 /-. A discount percentage of 5 on its listed price is announced. Therefore, the new selling price = Rs 450 – 5% of Rs 450 i.e. Rs 450 – Rs 22.5 = Rs 427.5/-**Cash Discount:**

Additional to trade discount, the manufacturer sometimes also offer discount called the Cash Discount if the buyers make complete payment within a certain time.

Cash Discount is offered on the net price (the price after subtracting the trade discount from marked price). Hence Cash Price = Net Price - Cash Discount

Tip: The cash discount is calculated on the net price unless specified.

**Wrong Weight:**When the trader professes to sell at the cost price (CP) but uses some false weight, then the percentage of profit earned = 100×Error/(True Weight-Error)**Successive Discounts:**When a trader offers more*than a*single discount to any customer, then sometimes you are asked to calculate the single discount that is equivalent to the two discounts offered. There one can apply the method of decimals learned in the percentages concept. Successive discounts are a part of regular lives as well as basic profit and loss mathematics. For Example, A trader offers two successive discounts of 20% & 10%. What is the single discount that is equal to the two successive discounts offered?

Let’s assume the market price is 100. A discount of 20% will leave 100 – 20 = Rs. 80/-. Now apply a further discount of 10%. So a discount of 10% on Rs. 80 is Rs 80 – Rs 8 = Rs. 72/-For Rs. 100 products, the final price is Rs. 72. And the total discount is Rs 100 – Rs 72 = Rs 28/-. The marked price is Rs. 100, the discount percentage is 100 × 28/100 = 28%. Here 28% is the single discount that is equal to two discounts of 20% and 10%. You can apply the percentage formula to find the single equivalent discount.**Single discount, equivalent to two successive discounts of m % and n % = M + N + MN/100.**

We need to take the discounts as negative in this formula; this can be positive or negative. In general, the discount is offered on the market price and it will reduce the market price. Its value is always taken in negative only. Let’s solve the same problem with the help of this formula.

The formula for profit and loss is very useful and important.

M + N + MN/100 ⇒ (-20) + (-10) + (-20)(-10)/100 ⇒ -20 – 10 + 2 = - 28.

Therefore the single equivalent discount is 28%.

*When the Selling Price (SP) of x articles is equal to the Cost price (CP) of y articles. What is the earned profit percentage?*

Profit percentage = 100× (difference in x and y)/x

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