# 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%

Explanation:

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

Gain = 28.60 – 27.50 = Rs. 1.10

Gain%=(GainCost100)%=(1.1027.50100)%=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%

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)

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.

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