# 16. GMAT Arithmetic Word Problems --- PROFIT AND LOSS Concept and Important Formulae

##
**PROFIT AND LOSS -- IMPORTANT FORMULAE**

This
chapter is as much important as other chapters in the arithmetic section, since
it is chapter of applications by which we calculate profit , loss , discount in
day to day business.

When
a person deals in the purchase and sale of any item, he either gains or loses
some amount generally. In day to day life we sell and purchase things as per
our requirement. A customer can get things in the following manner.

Manufacturer
-> Whole
sale -> Retailer

**Terminology:**

**Cost Price:**The cost price of an article is the price at which an article has been purchased. It is abbreviated as C.P

If
an article is purchased for some amount and there are some additional expenses
on transportation, labour cost, commission or repair charges etc. , these are to be added in the cost
price. Such expenses are called overhead expenses or overhead costs.

**Selling price:**The selling of an article is the rpice at which an article has been sold . It is abbreviated as SP

**Profit or gain:**If the selling price of an item is more than the cost price, there is a profit or gain.

Thus Profit or gain = Selling price –
Cost price SP > CP

**Loss:**If the cost price of an article is greater than that selling price, then there is a loss.

Thus Loss = Cost price – Sell Price CP > SP

**Some Important Formulae :**

**1)**

**Profit = SP – CP**

Example: A merchant bought an article for Rs 1250 and sold for
Rs 1400. What is the profit ?

Explanation: Cost price= Rs 1250 Selling price = Rs 1400

Profit = SP –CP = 1400 -1250=Rs
250

**2)**

**Loss = CP –SP**

Example: A person bought an article for Rs 1250 and sold for Rs
1175. What is the profit?

Explanation : Cost price= Rs 1250 Selling price = Rs 1175

Loss = CP –SP = 1250 – 1175 = Rs 75

**3)**

**Profit % = $\frac{Profit\%}{100}$ x 100%**

The cost price of a camera is Rs Rs 20000
and selling price is Rs 25000. Calculate
profit percentage.

Solution:
We have CP = Rs 20000 and SP= Rs
25000

Profit = SP – CP = Rs 25000
–Rs 20000 = Rs 5000

Profit % =

Profit
CP

x 100%
Profit% =

5000
20000

x 100% = 25%**4)**

**Loss % = $\frac{loss\%}{100}$ x 100%**

Sunil bought a gold ring for Rs 7500 and
sold it for Rs 6750. Find his loss percentage ?

Solution : Here CP = Rs 7500 SP = Rs 6750 CP> SP
So there is loss.

Loss = CP – SP = 7500 – 6750 = Rs 750

Loss % =

Loss
CP

x 100%
750
7500

x 100% = 10%**5)**

**Profit = CP X$ \frac{Profit\%}{100} $**

A man bought an article for Rs 2400 and sold at a profit of 10%.
What is the profit in rupees ?

Explanation : CP = Rs 2400 Profit % = 10%

Profit = CP x $ \frac{Profit\%}{100} $

= Rs 2400 x

10
100

= Rs 240

**6)**

**Loss = CP x**

loss%
100

Lakshmi bought an article for Rs 12000 and sold at a loss of
15%.What is his loss in rupees ?

Explanation : CP= Rs 12000 Loss % = 15

Loss =
CP x

loss%
100

Loss =
Rs 12000 x

15
100

= Rs 1800
Note
: Profit and loss are always calculated on the basis of cost price unless
otherwise mentioned in the problem.

**7)**

**When an article is sold at a profit%, then Selling price**

**Selling price = Cost price x**

(100+profit%)
100

Example : Mr Shastri buys a washing machine for Rs 9000. For how
much should he sell so that there is a gain of 8% ?

Explanation
: We have CP= Rs 9000 Gain % = 8%

Selling
price = Cost price x

(100+profit%)
100

= Rs 9000 x

(100+8)
100

= Rs 9000 x

108
100

= Rs 9720

**8) When an article is sold at a loss%, then Selling price**

**Selling price = Cost price x**

(100-loss%)
100

Example : Mr Sudheer buys a camera for Rs 9000 and sold at a
loss of 15%. Find the selling price?

Explanation : We have CP= Rs 9000 Loss % = 15%

Selling
price = Cost price x

(100-15%)
100

= Rs 9000 x

= Rs 9000 x

85
100

= Rs 7650

**9)**

**When the selling price and gain % is given , then cost price is**

**CP = SP X (**

100
(100+profit%)

)
Example: By selling an article for Rs 8400 , Kartik gains 20%. Find the cost price of the
article?

Explanation
: Here SP= Rs 8400 and Profit% = 20%

CP =
SP X
(

100
(100+profit%)

)
CP = Rs 8400 x 100/ 100+ 20

= Rs 8400 x 100/120

= Rs 7000

**10)**

**When selling price and loss% is given , then cost price is**

**CP = SP X (**

100
(100- Loss%)

)
Example: By
selling an article for Rs 6400 , Soumya
got a loss of 20%. Find the cost price
of the article?

Explanation : Here SP= Rs 6400 and Loss% = 20%

CP = SP X
(

100
(100- Loss%)

)
CP = Rs 6400 x

100
(100-20)

= Rs 6400 x

100
80

= Rs 8000

**Discounts :**

**Marked Price :**Basically to avoid loss due to bargaining by customer and to get profit over the cost price , seller increases the cost price by a certain value .

This
increase in value of over cost price is known as mark-up and the increased
price is (Cost price + Mark up) marked by the seller is called marked price or
printed price or list price. This price
is different from cost price and sale price.

Marked
Price = CP + Mark-up

Marked Price =
CP + (Percentage mark-up on CP)

The
amount by which the seller marks up the cost price can be expressed as a
percentage of the cost price. This percentage is called mark up percentage

Mark- up percentage =

Increase in the price
Cost price

x 100 %
Generally,
good are sold at marked price , if there is no further discount on the marked
price. In this (no discounts are given on market price ), the selling price and
marked price are equal.

Example : If the cost price of an article is Rs 600 and the
percentage markup is 25%. What is the marked price ?

Explanation: MP = CP + (% markup on
CP)

%
markup on CP = 600 x

25
100

= Rs 150

Marked price = 600 + 150

= Rs
750

**Discount :**The reduction made on the marked price of an article is called the discount

Discount
Percentage =

Discount
Marked Price

x
100%
The marked price of an article is Rs 1200 and a cash discount of
Rs.300 offered. What is the discount percentage?

Explanation : Discount = Rs
300 Market price = Rs 1200

Discount
Percentage =

Discount
Marked Price

x
100%
ð Discount%
= $\frac{300}{1200}$
X 100%

ð = 25%

When
marked price and discount percentage is given, then selling price is

SP = MP X

(100- Discount%)
100

Example : Marked price of an article is Rs 6600 and the discount
is 10%. Find the selling price ?

Explanation : Discount % = 10% Marked Price = Rs 6600

Selling price SP = Marked Price x

(100- Discount%)
100

= 6600 x

(100-10)
100

= 6600 x

= Rs 5940
90
100

**For Solved Examples on Profit and Loss ,**

**Solved**

**Problems on Profit and Loss 1**

For more solved problems ,

**Profit and Loss Solved Example 2**

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