Word Problems on Comparing Quantities

Class 8Comparing Quantities

The chapter Comparing Quantities covers ratios, percentages, profit and loss, discount, tax, compound interest, and simple interest. Word problems in this chapter require you to apply these concepts to real-life situations.

These problems involve shopkeepers calculating profit or loss, customers finding discounts, banks computing interest, and people comparing prices. Solving them requires identifying the correct formula and substituting the given values carefully.

This topic collects the most important types of word problems from the entire chapter for practice.

What is Word Problems on Comparing Quantities?

Key formulas used in word problems:

Profit = SP − CP (when SP > CP)
Loss = CP − SP (when CP > SP)
Profit % = (Profit/CP) × 100
Loss % = (Loss/CP) × 100
Discount = Marked Price − Selling Price
Discount % = (Discount/MP) × 100
SP after discount = MP × (1 − Discount%/100)
Sales Tax: Total cost = SP + (Tax% × SP)/100
SI = (P × R × T)/100
CI: A = P(1 + R/100)ⁿ

Types and Properties

Types of word problems:

Profit and loss: Finding CP, SP, profit%, loss%.
Discount: Finding selling price after discount on marked price.
Successive discounts: Two discounts applied one after another.
Tax problems: Finding total amount payable after adding VAT/GST.
Simple interest: Finding SI, principal, rate, or time.
Compound interest: Finding CI, amount, comparing CI and SI.
Mixed problems: Combining discount with tax, or profit with discount.

Solved Examples

Example 1: Example 1: Profit and loss

Problem: A shopkeeper buys an article for Rs 450 and sells it for Rs 540. Find the profit percentage.

Solution:

CP = Rs 450, SP = Rs 540
Profit = 540 − 450 = Rs 90
Profit % = (90/450) × 100 = 20%

Answer: Profit % = 20%.

Example 2: Example 2: Loss percentage

Problem: A bicycle bought for Rs 3,200 was sold for Rs 2,800. Find the loss percentage.

Solution:

CP = Rs 3,200, SP = Rs 2,800
Loss = 3200 − 2800 = Rs 400
Loss % = (400/3200) × 100 = 12.5%

Answer: Loss % = 12.5%.

Example 3: Example 3: Discount on marked price

Problem: A shirt has a marked price of Rs 1,200. A 15% discount is offered. Find the selling price.

Solution:

MP = Rs 1,200, Discount = 15%
Discount = 15% of 1200 = Rs 180
SP = 1200 − 180 = Rs 1,020

Answer: Selling price = Rs 1,020.

Example 4: Example 4: Successive discounts

Problem: A jacket with MP Rs 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 = Rs 1,440

Note: 20% + 10% successive discount ≠ 30% single discount. A 30% discount gives 2000 × 0.7 = Rs 1,400.

Answer: Final price = Rs 1,440.

Example 5: Example 5: Selling price with tax

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

Solution:

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

Answer: Total amount = Rs 17,700.

Example 6: Example 6: Finding CP from SP and profit%

Problem: A trader sells a watch for Rs 1,380 at a profit of 15%. Find the cost price.

Solution:

SP = CP × (1 + Profit%/100)
1380 = CP × (1 + 15/100) = CP × 1.15
CP = 1380/1.15 = Rs 1,200

Answer: Cost price = Rs 1,200.

Example 7: Example 7: SI word problem

Problem: Ravi deposited Rs 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 = Rs 1,800
Amount = P + SI = 8000 + 1800 = Rs 9,800

Answer: SI = Rs 1,800; Amount = Rs 9,800.

Example 8: Example 8: CI word problem

Problem: Find the compound interest on Rs 12,000 at 10% per annum for 2 years.

Solution:

A = P(1 + R/100)ⁿ = 12000(1.1)² = 12000 × 1.21 = Rs 14,520
CI = A − P = 14520 − 12000 = Rs 2,520

Answer: CI = Rs 2,520.

Example 9: Example 9: Discount + Tax combined

Problem: An item has MP = Rs 5,000. A discount of 10% is offered. Then 12% GST is charged. Find the final price.

Solution:

After discount: 5000 × 0.9 = Rs 4,500
After GST: 4500 × 1.12 = Rs 5,040

Answer: Final price = Rs 5,040.

Example 10: Example 10: CI vs SI comparison

Problem: Find the difference between CI and SI on Rs 20,000 at 8% per annum for 2 years.

Solution:

SI = (20000 × 8 × 2)/100 = Rs 3,200
CI: A = 20000(1.08)² = 20000 × 1.1664 = Rs 23,328
CI = 23328 − 20000 = Rs 3,328
Difference = 3328 − 3200 = Rs 128

Shortcut: CI − SI (for 2 years) = P(R/100)² = 20000 × (0.08)² = 20000 × 0.0064 = Rs 128 ✓

Answer: Difference = Rs 128.

Real-World Applications

Where these problems appear in real life:

Shopping: Calculating discounts, comparing prices, and finding final amounts after tax.
Banking: Computing interest on savings, loans, and fixed deposits.
Business: Calculating profit margins, setting prices, and managing costs.
GST billing: Every purchase includes tax calculation.

Key Points to Remember

Profit% and Loss% are always calculated on CP (cost price).
Discount% is calculated on MP (marked price).
Tax is added after discount.
Successive discounts of a% and b% ≠ (a+b)% single discount.
CI − SI for 2 years = P(R/100)².
Always check: is the question asking for SI or CI?
For finding CP from SP, divide: CP = SP/(1 + Profit%/100).
Read word problems carefully to identify what is given and what is asked.

Practice Problems

A shopkeeper buys goods for Rs 6,000 and sells them for Rs 6,900. Find the profit %.
A toy marked at Rs 800 is sold at 25% discount. Find the selling price.
Find the SI on Rs 15,000 at 9% for 2 years.
An item costs Rs 2,500 after a discount of 20%. What was the marked price?
Find the CI on Rs 10,000 at 12% for 3 years compounded annually.
Successive discounts of 15% and 10% are given on an item with MP Rs 4,000. Find the final price.
A laptop is sold for Rs 36,000 at a loss of 10%. Find the cost price.
A bill of Rs 8,000 has 5% GST. Find the total amount payable.

Frequently Asked Questions

Q1. How do I identify which formula to use?

Read the problem carefully. If it mentions CP and SP → profit/loss. If it mentions MP → discount. If it mentions principal, rate, time → interest.

Q2. Are successive discounts the same as adding the percentages?

No. 20% + 10% successive discounts give a final price different from a single 30% discount. Apply each discount one after the other.

Q3. Is GST applied before or after discount?

GST is applied AFTER the discount. First reduce the price by the discount, then add GST on the reduced price.

Q4. When is CI greater than SI?

CI is always greater than SI when the time is more than 1 year (at the same rate). For exactly 1 year with annual compounding, CI = SI.

Q5. How do I find CP when SP and profit% are given?

Use: CP = SP ÷ (1 + Profit%/100). For loss: CP = SP ÷ (1 − Loss%/100).

Q6. What is the difference between marked price and cost price?

Cost price (CP) is what the seller paid. Marked price (MP) is the listed/tag price. The seller may mark up the price above CP before offering a discount.

Word Problems on Comparing Quantities

What is Word Problems on Comparing Quantities?

Types and Properties

Solved Examples

Example 1: Example 1: Profit and loss

Example 2: Example 2: Loss percentage

Example 3: Example 3: Discount on marked price

Example 4: Example 4: Successive discounts

Example 5: Example 5: Selling price with tax

Example 6: Example 6: Finding CP from SP and profit%

Example 7: Example 7: SI word problem

Example 8: Example 8: CI word problem

Example 9: Example 9: Discount + Tax combined

Example 10: Example 10: CI vs SI comparison

Real-World Applications

Key Points to Remember

Practice Problems

Frequently Asked Questions

Q1. How do I identify which formula to use?

Q2. Are successive discounts the same as adding the percentages?

Q3. Is GST applied before or after discount?

Q4. When is CI greater than SI?

Q5. How do I find CP when SP and profit% are given?

Q6. What is the difference between marked price and cost price?

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