Problems On Profit And Loss

 

Profit and Loss: The Basics

• Profit: Occurs when a business sells a product or service for more than it cost to buy. It represents financial gain.
• Loss: Occurs when a business sells a product or service for less than its cost price. It represents financial deficit.

The Key Formulas

• Profit = Selling Price (SP) - Cost Price (CP)
• Loss = Cost Price (CP) - Selling Price (SP)
• Profit Percentage (%) = (Profit / CP) × 100
• Loss Percentage (%) = (Loss / CP) × 100

8 Simple Practice Questions & Solutions

Q1. Simple Profit

A shopkeeper buys a book for $200 and sells it for $250. Find the profit.

Solution:
CP = $200, SP = $250
Profit = SP - CP = 250 - 200 = 50
Answer: The profit is $50.

Q2. Simple Loss

A cycle bought for $1,200 is sold for $1,000. Find the loss.

Solution:
CP = $1,200, SP = $1,000
Loss = CP - SP = 1200 - 1000 = 200
Answer: The loss is $200.

Q3. Profit Percentage

An item bought for $80 is sold for $100. Find the profit percentage.

Solution:
CP = $80, SP = $100
Profit = 100 - 80 = 20
Profit % = (20 / 80) × 100 = 25%
Answer: The profit percentage is 25%.

Q4. Loss Percentage

A toy bought for $50 is sold for $40. Find the loss percentage.

Solution:
CP = $50, SP = $40
Loss = 50 - 40 = 10
Loss % = (10 / 50) × 100 = 20%
Answer: The loss percentage is 20%.

Q5. Finding Selling Price (Profit)

A man buys a watch for $500 and wants to make a 10% profit. What should the selling price be?

Solution:
CP = $500, Profit % = 10%
Profit Amount = 10% of 500 = $50
SP = CP + Profit = 500 + 50 = 550
Answer: The selling price should be $550.

Q6. Finding Selling Price (Loss)

A table bought for $300 is sold at a loss of 15%. Find the selling price.

Solution:
CP = $300, Loss % = 15%
Loss Amount = 15% of 300 = $45
SP = CP - Loss = 300 - 45 = 255
Answer: The selling price is $255.

Q7. Finding Cost Price (Profit)

An article is sold for $120 at a profit of 20%. Find its cost price.

Solution:
SP = $120, Profit % = 20%
SP = CP × 1.20 → 120 = CP × 1.20
CP = 120 / 1.20 = 100
Answer: The cost price is $100.

Q8. Finding Cost Price (Loss)

By selling a bag for $90, a shopkeeper incurs a loss of 10%. Find the cost price.

Solution:
SP = $90, Loss % = 10%
SP = CP × 0.90 → 90 = CP × 0.90
CP = 90 / 0.90 = 100
Answer: The cost price is $100.