Profit and loss is a topic from the CAT quantitative ability section and almost 3-4 questions are asked every year in the exam. To help the candidates prepare the profit and loss topic, here are all the related details, formulae and solved examples.

**Terminologies Involved in Profit & Loss:**

**1) Cost Price (CP):**

The amount paid to buy a product or the cost involved in manufacturing a product is called the * Cost Price (CP)* of that product.

**2) Selling Price (SP):**

The price at which an article is sold to the customer.

**3****) Marked Price (MP):**

The price which the shopkeeper fixes for the product (the price on the label) in anticipation of some discount they may be asked by the customer for the product.

**4) Discount:**

The reduction made on the marked price is called the discount. When no discount is given, the * Selling Price = Marked Price*.

**5) Margin:**

When profit percentage is calculated as a percentage of SPM then it is known as margin.

**6) Types of cost:**

** a) Fixed Cost**➜ The kind of cost which is fixed in all cases

**b) Variable cost**➜ The cost which varies according to the number of units produced

**c) Semi-Variable cost**➜ Cost which is fixed for some entities and variable for some entities.

**Important:**

**Profit and Loss is always calculated on Cost Price.**

%Profit = Profit/CP x100 = (SP-CP)/CP x 100 = ((SP/CP)– 1)x100

% Loss= Loss/CP x100 = (CP-SP)/CP x100 = ((1-SP/CP) )x100

Discount is always calculated on Marked Price.

% Discount= Discount/MP x100.

**Other Profit & Loss Formulae Involved:**

**(a)** Profit = SP-CP (SP>CP)

**(b)** Loss= CP-SP (CP>SP)

**(c)** SP= MP- discount

**(d)** MP = SPx100/(100 – discount%)

**(e)** If two items are sold at the same price, one with a profit of x% and another with a loss of x%, there will be an overall loss given by x^{2}/100.

**(f)** If the CP of two items is the same, and one is sold at x% gain, other at x % loss, then the net loss or net profit=0.

**(g)** On an offer of buy “a” goods and get “b” goods free, i.e., if “a+b” articles are sold at the rate of “a” articles,

then the percentage discount = [(b/(a+b))×100]

**(h)** If there are successive discounts of x% and y%, the effective discount can be calculated as [x+y – (xy/100) ]%

**(i)** There are many shopkeepers who cheat by using false weights, then the gain to the shopkeeper on using the false weight can be calculated as follows (100 + Gain%)/100=(True Weight)/(False Weight).

**Explanation:**

Suppose the shopkeeper is using a false weight in such a way that when his meter shows X kg (False weight) he is actually selling Y kg (True weight). Also say that the price he is selling the article is Rs. Z per kg. Thus, when his meter is showing X kg, he is actually selling Y kg. So for the shopkeeper, the cost price (CP) = YZ

But the selling price (SP) = XZ

So, his profit = (SP – CP)/CP=(XZ – YZ)/YZ = X/Y– 1or (X/Y– 1)x100 %

➜(Profit%)/100=X/Y– 1

**Illustrations on Profit & Loss Shortcut Tricks:**

**1) Monte Carlo is offering a summer discount of 20% on all the sweaters. Ram buys sweaters which cost him Rs. 3000/- and then resold them in his shop at a discount of 10% on the market price. Find the total profit he earned.**

**Solution: **

When Ram bought sweaters from Monte Carlo he paid Rs. 3000.Thus, 3000 is Ram’s Cost Price Using MP = SPx100/(100 – discount%)

MP = (3000 x 100)/(100 – 20) = 3000 x 100/80 = 3750. Rs 3750 is now, the new Marked Price

He sold all sweaters at a discount of 10%; discount = 10 x 3750/100 = Rs. 375.

So he sold the sweaters at Rs. 3750 – Rs. 375 = Rs. 3375. Profit = Rs. (3375 – 3000) = Rs. 375.

**2) In the previous question, calculate the profit percentage earned by Ram.**

**Solution: **

Profit earned = Rs. 375 Cost Price (CP) for Ram = Rs. 3000 So profit percentage = 375 ×100/3000 = 12.5%.

**3) The CP of 40 articles = SP of 50 articles. What is the profit or loss percentage?**

**Solution: **

Since the Cost Price of 40 articles= Selling Price of 50 articles, we realize that the transaction is a loss for the shopkeeper.

CP will be greater than SP

CP/SP=50/40=5/4

Loss percentage = (1-SP/CP)x100

Loss Percentage = (1-4/5)=1/5 x 100= 20%.

**4) A shopkeeper sells two shirts at the same price; one at a discount of 20% and another at a gain of 20%.Find the overall loss or the gain he earned.**

**Solution:**

As both shirts are sold at the same price one at 20% loss and other at 20% profit, he will make a net loss of 20^{2}/100= 4%

**Note:- **

**Although formulas are given for different cases, this is just for your reference. It is always better to approach every question by assuming values or going from answer options.**

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