Word Problems on Profit and Loss
Profit and loss word problems involve buying and selling. When the selling price (SP) is more than the cost price (CP), there is a profit. When SP is less than CP, there is a loss.
These problems are common in daily life — shopkeepers, businesses, and individuals calculate profit and loss regularly.
What is Word Problems on Profit and Loss - Grade 7 Maths (Comparing Quantities)?
Key formulas:
- Profit = SP − CP (when SP > CP)
- Loss = CP − SP (when CP > SP)
- Profit % = (Profit/CP) × 100
- Loss % = (Loss/CP) × 100
Word Problems on Profit and Loss Formula
Finding SP from profit% or loss%:
SP = CP × (100 + Profit%)/100 | SP = CP × (100 − Loss%)/100
Types and Properties
Common question types:
- Find profit or loss from given CP and SP.
- Find profit% or loss%.
- Find SP when CP and profit% are given.
- Find CP when SP and profit% or loss% are given.
Solved Examples
Example 1: Finding Profit and Profit%
Problem: A shopkeeper buys a toy for ₹250 and sells it for ₹300. Find the profit and profit%.
Solution:
- Profit = 300 − 250 = ₹50
- Profit% = (50/250) × 100 = 20%
Answer: Profit = ₹50, Profit% = 20%.
Example 2: Finding Loss%
Problem: A phone bought for ₹15,000 was sold for ₹12,000. Find the loss%.
Solution:
- Loss = 15000 − 12000 = ₹3000
- Loss% = (3000/15000) × 100 = 20%
Answer: Loss% = 20%.
Example 3: Finding SP from Profit%
Problem: CP of a book is ₹400. It is sold at 15% profit. Find the SP.
Solution:
- SP = 400 × (100 + 15)/100 = 400 × 115/100 = ₹460
Answer: ₹460.
Example 4: Finding CP from SP and Loss%
Problem: An item was sold for ₹680 at a loss of 15%. Find the CP.
Solution:
- SP = CP × (100 − 15)/100
- 680 = CP × 85/100
- CP = 680 × 100/85 = ₹800
Answer: CP = ₹800.
Real-World Applications
Real-world uses:
- Business: Calculating margins, pricing products.
- Shopping: Comparing deals, understanding markups.
- Stock market: Profit/loss on buying and selling shares.
Key Points to Remember
- Profit and loss are always calculated on the cost price (CP).
- Profit% = (Profit/CP) × 100.
- Loss% = (Loss/CP) × 100.
- If SP > CP → Profit. If CP > SP → Loss.
- SP = CP + Profit = CP − Loss.
Practice Problems
- A bicycle bought for ₹4,500 is sold for ₹5,400. Find the profit%.
- A TV is bought for ₹20,000 and sold at 10% loss. Find the SP.
- SP = ₹540, Profit% = 8%. Find CP.
- CP = ₹1,200, Loss = ₹180. Find loss%.
Frequently Asked Questions
Q1. How do you calculate profit percentage?
Profit% = (Profit ÷ Cost Price) × 100. Profit = Selling Price − Cost Price.
Q2. On what value is profit/loss percentage calculated?
Always on the Cost Price (CP), not on the Selling Price.
Q3. How do you find SP when CP and profit% are given?
SP = CP × (100 + Profit%)/100. For loss: SP = CP × (100 − Loss%)/100.
Related Topics
- Profit and Loss
- Discount Calculation
- Introduction to Percentage
- Simple Interest
- Percentage Increase and Decrease
- Compound Interest
- Applications of Compound Interest
- Sales Tax and VAT
- Growth and Decay
- Finding Percentage of a Number
- Converting Between %, Fraction and Decimal
- Word Problems on Comparing Quantities
- Converting Percentage to Fraction
- Compound Interest (Half-Yearly & Quarterly)
