Word Problems on Comparing Quantities

Word problems on comparing quantities covers concepts of ratios, percentages, profit and loss, discount, tax, compound interest, and simple interest. The word problems based on comparing quantities topic require understanding of these concepts and their applications in real-life situations.

These problems involve calculating profit, loss, discounts, interests, and comparing prices. Solving these problems requires understanding the concept and identifying the correct formula to substitute the given values carefully. 

 

Table of Contents

• Types of Word Problems on Comparing Quantities
• Formulas To Solve Word Problems on Comparing Quantities
• Solved Examples

Types of Word Problems on Comparing Quantities

Before looking at word problems on comparing quantities we need to understand the key formulas and types of problems covered under different concepts. 

• Word problems based on finding CP, SP, profit% and loss%.

• Word problems based on finding selling price after discount on market price.

• Word problems based on discounts applied one after another.

• Word problems based on finding VAT/GST.

• Word problems based on finding Simple Interest, principal, rate, or time.

• Word problems based on finding amount and SI.
  
  

Formulas To Solve Word Problems on Comparing Quantities

The list of key formulas used in solving problems on comparing quantities is given below:

Solved Examples

Problem 1: Reeta purchases an item for ₹400 and sells it for ₹450. Find the percentage of profit Reeta earned.

Solution: Cost Price = ₹400 and Selling Price = ₹450
By using the formula of profit: Profit = 450 − 400 = ₹50
To find the profit percentage use formula: Profit % = (Profit/CP) × 100
Profit % = (50/400) × 100 = 12.5%

Therefore, Profit % = 12.5%.

Problem 2: Rohan bought a toy for ₹400 and sold for ₹100. Find the loss percentage.

Solution: Cost Price of toy = ₹400, Selling Price of toy = ₹100
The loss in selling toy is equal to CP – SP = 400 − 100 = ₹300
Loss % = (300/400) × 100 = 75%

Therefore, Loss % = 75%.

Problem 3: A dress has a cost price of ₹1,000 and store discount is 15%. Calculate the selling price of dress after discount.

Solution: Marked price of dress = ₹1,000
Discount offered on market price = 15%
Discount = 15% of 1000 = Rs 150
Selling Price after discount = 1000 − 150 = ₹859

Therefore, Selling price = ₹850

Problem 4: A blazer with marked price of ₹2,000 is offered 20% + 10% successive discounts. Find the final price.

Solution: After 1st discount (20%): 2000 × (1 − 20/100) = 2000 × 0.8 = Rs 1,600
After 2nd discount (10%): 1600 × (1 − 10/100) = 1600 × 0.9 = ₹1,440
Final price = ₹1,440.
 

Problem 5: A phone costs ₹15,000. GST is 18%. Find the total amount to be paid.

Solution: Price = ₹15,000, GST = 18%
Tax = 18% of 15000 = ₹2,700
Total = 15000 + 2700 = ₹17,700

Total amount = ₹17,700.

Problem 6: An item is priced at ₹5,000. A discount of 10% is offered. Then 12% GST is charged. Find the final price.
Solution: Price of item = ₹5,000 and Discount offered = 10 %
Price of item after discount: 5000 × 0.9 = ₹4,500
Price of item after GST: 4500 × 1.12 = ₹5,040

Final price of item = ₹5,040.

Problem: Ravi deposited ₹8,000 in a bank at 7.5% per annum for 3 years. Find the simple interest and total amount.
Solution: SI = (P × R × T)/100 = (8000 × 7.5 × 3)/100 = ₹1,800
Amount = P + SI = 8000 + 1800 = ₹9,800
SI = ₹1,800
Amount = ₹9,800.