Profit and Loss

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 x2/100.

(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 202/100= 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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