# Profit and Loss | Formulas, Concepts and Tricks on Profit & Loss

## Profit and Loss

When we buy a thing by paying some money and sell it back, then definitely we will be in either profit or loss. This profit and loss depends on selling Price and cost price. #### Cost Price (C.P.):

The price, at which an article is purchased, is called its cost price, abbreviated as C.P.

#### Selling Price (S.P.):

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

Profit and Loss Definition:

### Profit or Gain:

When selling price is more than that of cost price, then it is called profit. Formally, it can be given as
Profit = selling price(S.P.) – cost price(C.P.).
OR
If S.P. > C.P., it is a profit or gain

### Loss:

When cost price is more than selling price, then it will be known as loss and it can be given as

Loss = cost price(C.P.) – selling price(S.P.).
OR
If C.P. > S.P., it is a loss.

Loss or gain is always reckoned on C.P.

### Gain Percentage: Gain(%) ### Loss Percentage: Loss(%) ### In the case of a Loss, ### • #### If a trader professes to sell his goods at cost price, but uses false weights, then ## Profit and Loss Problems

Example 1:

A book was purchased at 100. It was sold at 120. What is profit percent?

Solution:

C.P. = 100 and S.P. = 120. Profit = 120 ― 100 = 20.

Profit % = [(Profit/C.P.) × 100] %

Hence, gain (%) = (20/100) × 100 % = 20%

Example 2:

A boy purchased a pen at 20. He sold it his friend for 15. What is the loss he made in percentage?

Solution:

C.P. = 20 and S.P. = 15 and Loss = 20 ― 15 = 5

Loss % = [(Loss/C.P.) × 100] %

Hence, Loss (%) = (5/20) × 100 % = 25%
Example 3 :

The cost of 11 pencils is equal to the selling price of 10 pencils. Find the loss or profit percent, whatever may be the cost of 1 pencil.

Solution : The cost price of 11 pencils = S.P of 10 pencils

Let C.P of 1 pencil is 1 .

C.P of 10 pencils = 10

S.P of 10 pencils = C.P of 11 pencils = 11

Profit on 10 pencils = 11 – 10 = 1

Hence, Profit % = ( 1/ 10) x 100 = 10 %

Example 4:

Sam sold his Mobile Phone a loss of 20%. If he had sold it for 800 more, he would have received a profit of 5%. Find the cost price .

Solution :
Let the cost price be 100
So when C.P = 100 , loss of 20% means
S.P = 100 – 20 = 80
Profit of 5% means S.P = 100 + 5 = 105
The difference of two S.P = 105 – 80 = 25

If the difference is 25, C.P = 100

If the difference is \$ 800 , C.P = (100 / 25 ) x 800
C.P = 3200

Hence Cost Price will be 3200

Example 5:

A reduction of20% in the price of sugar enables Mrs. Jones to buy an extra 5 kg of it for  320.

Find:
(i) the original rate, and
(ii) the reduced rate per kg.

Solution:

Let the original rate be \$ x per kg.

Reduced rate = (80% of \$ x) per kg

=  (x × 80/100) per kg

Quantity of sugar for \$ 320 at original rate = 320/x kg

Quantity of sugar for \$ 320 at the new rate = 320/(4x/5) kg

= (320 × 5)/4x kg

= 400/x kg.

Therefore, (400/x) – (320/x) = 5

⇔ 5x = (400 – 300)

⇔ 5x = 80

⇔ x = 16

(i) Original rate = \$ 16 per kg

(ii) Reduced rate = (4/5 × 16) per kg

=  64/5 per kg

=  12.80 per kg.

In the video Given below you will learn some better ways to calculate Profit and loss Problems