Profit and Loss

Profit and Loss

Cost price

Cost price is defined as price at which an article is purchased.

Selling price

Selling price is defined as price at which an article is sold.

Profit

If Selling Price is more than Cost Price, then there is profit SP > CP, (Selling price is greater than Cost Price)

Profit = ( SP - CP )

Loss

If Selling Price is less than CP then there has been a loss occurred. SP < CP, (Selling price is less than Cost Price)
Loss = (CP - SP )

Basic Formulas

1. Profit = ( SP - CP )
2. SP = ( profit + CP )
3. CP = (SP - profit)
4. Profit % = ( profit * 100 ) / CP
5. SP = CP*[1+(profit%/ 100)]
6. CP = ( 100*SP ) / ( 100 * profit%)
7. Loss = ( CP - SP )
8.SP =(CP - loss)

9. CP=(SP+ loss)
10. Loss % = ( loss * 100 ) / CP

Example sum

1. Arjun buys an mobile cover for Rs. 100 and sells it for Rs. 110. Find him profit?
Cost price = Rs. 100
Selling price = Rs. 110
Profit = Selling Price - Cost Price
= (110-100)
= Rs. 10

2. Arjun buys an mobile cover for Rs. 100 and sells it for Rs. 80. Find his Loss?
Cost price = Rs. 100
Selling price = Rs. 80
Loss = Cost Price - Selling Price
= Rs. (100 - 80)
= Rs. 20

3. Arjun buys an mobile cover for Rs. 100 and sells it for Rs. 110. Find him profit percent?
Cost price = Rs. 100
Selling price = Rs. 110
Profit = Selling Price - Cost Price
= Rs. (110- 100)
= Rs. 10
Profit % = [(10/ 100) * 100]

=10%

4. Arjun buys an mobile cover for Rs. 100and sells it for Rs. 80. Find his Loss percent?
Cost price = Rs. 100
Selling price = Rs. 80
Loss = Cost Price - Selling Price

= Rs. (100 - 80)
= Rs. 20
Loss % = [ (20 /100 ) * 100]%
= 20%

5. Selling price of an article is Rs. 2220 and the percent profit earned is 20%. What is the cost price of the article?
Selling Price ( SP ) = 2220
Profit percentage = 20%
Cost Price ( CP) = [ 100 / ( 100 +Gain %)] * Selling price
=[100/(120)]* 2220
= 370 * 5
=Rs. 1850

General Terms:

• If two articles are sold first article at x% profit and the second article at y% loss, thus making no profit, no loss in the transaction, Then cost price of the two articles are in the ratio y : x

Proof:
Profit on the first article = ax / 100
Loss on the second article = by / 100
There is no profit or no loss in the bargain. =ax/ 100 = by / 100
ax = by
a/b=y/x

Example sum:A man purchased two articles for total cost of Rs. 9000. He sold the first article at 15% profit and the second at 12% loss. In the bargain, he neither gained nor lost anything. Find cost price of the first article.

Ratio of cost price of the first and the second article = 12 : 15

= 4:5
Cost price of the first article

= (4/ 9) *9000= 4*1000

= Rs.4000

• If two article are sold at equal prices,the first one is sold at P1% Profit and whereas the second one at a Profit of P2% And the sum of the cost price of twoarticle is x, then
  
• Cost price of an article at profit P1% = [ (100+P2/(200+P1+P2)]*x

Example sum:A trader bought two watches for Rs 2300. He sold one at a profit of 10% and the other at a profit of 20%. If the selling price of each watch is the same, then their cost
price are respectively.
Cost price of an article at profit P1% = [ (100+P2/(200+P1+P2)]*x

P1=10%

P2=20%

x = Rs. 2300
Cost price of a watch at profit of 10%=[(100+20)/(200+10+20)]* 2300
= 120*10
= Rs. 1200
Cost price of a watch at profit of 20% = 2300 - 1200
= Rs. 1100