Topic:: Important facts and formula of Profit and Loss with Examples

Read conceptual problems, formulas and shortcuts tips and tricks of Profit and Loss for SSC, IBPS PO/CLERK, RRB, CSAT, CAT Exam and other MBA exams.

Important facts that you should memorize

Cost Price : The price at which any article is purchased is called its cost price, abbreviated as C.P.

Selling Price : The price, at which an article is sold, is called its selling prices, abbreviated as S.P.

Profit : If Selling Price is greater than Cost Price then seller makes profit.

                                Profit = SP – CP

Loss : If Cost Price is greater than Selling Price then seller incurs loss.

                                Loss = CP – SP

• If an article is sold at a gain of 50%, than it means  then S.P. = 150% of C.P.
• If an article is sold at a loss of 40% then S.P. = 60% of C.P.

Profit and loss calculations are extensions of percentage only with a few twists thrown in because of play of words. In SSC, RRB, CSAT and MBA exams, approaching these problems in a straight and simplified manner can save you much time. So we will discuss some important formulae.

Important Formulae of Profit and Loss

Gain Percentage (Gain %)   

Loss Percentage (Loss %) 

Selling Price (S.P.) in case of loss %

Selling Price (S.P.) in case of gain % 

Cost Price (C.P.) in case of gain % 

Cost Price (C.P.) in case of loss % 

Quicker approach for tricky problems/Shortcuts

Rule 1: When a person sells two similar items, one at a gain of say x%, and the other at a loss of x% than theloss incurred by the seller is given by

Loss % =   

Rule 2 : If a trader professes to sell his goods at cost price, but uses false weights, then :

Gain % =        

Rule 3 : If there are two successive profits of R1% and R2% then total profit % =

 

Rule 4 : If there  is a profit of R1% and loss of R2% then total profit or loss % =

Rule 5 : If the cost price of P article is equal to selling price of Q article where P>Q, then profit % :

Rule 6 : If a person marks his article P% above it’s cost price and gives customers a discount of Q% then net profit of loss % is :

Solved examples on Profit and Loss

Q1. A motorbike vendor recovers the cost of 25 bikes by selling 20 bikes. Find the % profit

(a) 20 %                      (b) 25 %                      (c) 15 %                       (d) 16 %

Solution:

Here in this case price of quantity soled and Cost price are equal, so

Q2. Jethalal bought a Nokia mobile phone @ Rs. 800. He sold it to Master Bhide after allowing a discount of 10%. In this deal, Jethalal made a profit of 12.5%. What was the marked price?

1. Rs. 1,000
2. Rs. 1,100
3. Rs. 1,200
4. Rs. 1,300

Solution

Profit is always calculated on actual investment (cost price).
Cost Price: Rs.800
The question says, profit =12.5%. What is the profit in rupee terms?

Long cut	Shortcut
=12.5% x 800 =(125/10)x (1/100) x 800 =Rs. 100	12.5% =1/8 (percentage to fraction conversion table). So, 12.5% x800 = (1/8) x 800= Rs. 100

Anyways in either method, profit is Rs.100…Fact (i)
Jethalal gave 10% discount on marked price. So customer Bhide Master had to pay only
90% of the Marked Price.
=0.9 times the marked price
=this is the money Jethalal received from customer.

Jethalal’s actual profit

=the money he received from customer MINUS his original investment.
=0.9 times Marked price MINUS Rs.800
But recall fact (i), Jethalal’s profit is Rs.100
Therefore
100=0.9 times Marked price – Rs.800
100+800=0.9 times marked price
900=0.9 x MP
MP=900 x 10/9
MP=Rs. 1000.
Final Answer: marked price is Rs.1000

In the exam hall, directly frame the equation: 0.125 x800 =(0.9 xMP)-800

Q3. A man buys an article for Rs. 27.50 and sells it for Rs 28.60. Find his gain percent

• 1%
• 2%
• 3%
• 4%

Answer with Explanation

Answer: Option D

Explanation:

So we have C.P. = 27.50
S.P. = 28.60

Gain = 28.60 – 27.50 = Rs. 1.10

Gain%=(GainCost∗100)%=(1.1027.50∗100)%=4%

Q4. A fruit vendor fixed his selling price of mangoes at 40 % above the cost price. He sells half of the stock of mangoes at this price, now he offers a discount of 15 % on original selling price for one quater of stock and rest at a discount of 30 % on original selling price. Find the gain percentage altogether ?

(a) 20.30 %                      (b) 21.22 %                      (c) 25.45 %                       (d) 24.25 %

Let the Cost Price of mangoes be 100 , then Selling Price be 140

So, gain percentage = 24.25 % , option (d) is correct

Q5. If the cost price is 25% of selling price. Then what is the profit percent.

1. 150%
2. 200%
3. 300%
4. 350%

Answer: Option C

Explanation:

Let the S.P = 100
then C.P. = 25

Profit = 75

Profit% = 75/25 * 100 = 3005

The question given below is a sample practice problem in Profits, Discounts and Markup. It is an Arithmetic Topic and the problem provides an understanding of the core concept related to profits and discounts.

Q6. A merchant marks his goods in such a way that the profit on sale of 50 articles is equal to the selling price of 25 articles. What is his profit margin?

1. 25%
2. 50%
3. 100%
4. 66.67%

Correct Answer – 100% profit. Choice (3)

Answer with Explanation

Let the selling price per article be = Re. 1
Therefore, selling price of 50 articles = Rs.50

Profit on sale of 50 articles = selling price of 25 articles = Rs.25.
S.P = 50. Profit = 25. Therefore, CP = 50 – 25 = 25.

 .

Correct answer choice (3)

Practice more questions as much as you can from your books. Collection of above questions that typically appear from the topic profit, loss and discounts in Indian Business Schools entrance tests such as IBPS, RRB, SSC, CAT, XAT and TANCET. You can download

NCERT PDF for this chapter:… click here

NIOS PDF FOR PERCENTAGE AND ITS APPLICATION:… click here