Profit and Loss

Profit and loss deal with the comparison between cost price (CP) and selling price (SP) of an article. If SP is greater than CP, there is profit. If SP is less than CP, there is loss. These concepts are widely used in daily life such as buying and selling goods, business transactions, and trade.

Cost Price (CP)

Cost Price is the price at which an article is bought.
It includes all expenses like transportation, tax, loading, unloading, etc.

Example:
If a book is bought for Rs. 100 and transportation cost is Rs. 10, then
CP = Rs. 110

Selling Price (SP)

Selling Price is the price at which an article is sold.

Profit

When Selling Price is greater than Cost Price, the difference is called profit.

Actual Profit = SP − CP

Loss

When Selling Price is less than Cost Price, the difference is called loss.

Actual Loss = CP − SP

Profit Percent

Profit percent shows how much profit is made compared to cost price.

Profit % = (Profit / CP) × 100%

Loss Percent

Loss percent shows how much loss is made compared to cost price.

Loss % = (Loss / CP) × 100%

Relationship Between CP and SP

If profit is P%
SP = CP × (100 + P) / 100

If loss is L%
SP = CP × (100 − L) / 100

Finding Cost Price

If SP and profit percent are given:

CP = (SP × 100) / (100 + Profit%)

If SP and loss percent are given:

CP = (SP × 100) / (100 − Loss%)

Daily Life Problems on Profit and Loss

Profit and loss problems appear in daily life while buying or selling goods like food items, clothes, books, machines, etc. These problems can be solved by identifying CP, SP, profit or loss, and then applying suitable formulas.

Problem Solving Steps

Understand the problem

Write given information

Identify what is to be found

Apply correct formula

Check calculation

Write final conclusion

Formula Table:

Solved Important Questions 

Question1.

Sabita bought a bag for Rs. 500 and sold it at 25% profit. Find SP.

Profit = 25% of 500 = 125
SP = 500 + 125 = Rs. 625

Question2.

Kabir bought a watch for Rs. 4000 and sold it for Rs. 3200. Find loss percent.

Loss = 4000 − 3200 = 800
Loss % = (800 / 4000) × 100 = 20%

Question3.

A man bought an article for Rs. 600 and sold it for Rs. 690. Find profit percent.

Profit = 690 − 600 = 90
Profit % = (90 / 600) × 100 = 15%

Question4.

Selling price of an article is Rs. 840 with 12% profit. Find CP.

CP = (840 × 100) / 112
CP = Rs. 750

Question5.

Selling price of an article is Rs. 680 with 15% loss. Find CP.

CP = (680 × 100) / 85
CP = Rs. 800

Question6.

A trader bought 40 pens for Rs. 800 and sold them at Rs. 25 each. Find profit or loss per pen.

CP per pen = 800 / 40 = 20
SP per pen = 25
Profit per pen = Rs. 5

Question7.

A fruit seller bought 30 kg apples at Rs. 80 per kg and sold all for Rs. 2700. Find profit percent.

CP = 30 × 80 = 2400
Profit = 2700 − 2400 = 300
Profit % = (300 / 2400) × 100 = 12.5%

Question8.

An article is sold at 10% loss for Rs. 450. Find CP.

CP = (450 × 100) / 90
CP = Rs. 500

Question9.

A shopkeeper gains 20% by selling an article for Rs. 720. Find CP.

CP = (720 × 100) / 120
CP = Rs. 600

Question10.

If cost price of an article is Rs. 1500 and selling price is Rs. 1350, find loss percent.

Loss = 1500 − 1350 = 150
Loss % = (150 / 1500) × 100 = 10%

For further practice visit this link !!

https://besidedegree.com/exam/s/academic