Exam Prep

Comparing Quantities for Math Olympiad: Complete Preparation Guide

Percentages, profit-loss, interest — real-world math at Olympiad level!

OlympiadClass 7Class 8
SparkEd Math18 March 20269 min read
Visual guide to Comparing Quantities for Math Olympiad

Why Comparing Quantities Matters in Olympiads

Comparing quantities — percentages, profit-loss, interest, discounts — is where math meets the real world. Olympiad papers love these topics because they test both mathematical skills and practical reasoning.

For Class 7-8 students, competition problems often involve multiple concepts combined. A single problem might mix percentage increase with profit calculation and discount application, requiring careful step-by-step thinking.

Best Preparation Strategy

Master comparing quantities for competitions:

Step 1: Percentage Fluency

Be able to convert between fractions, decimals, and percentages instantly. Know common equivalents: 14=25%\frac{1}{4} = 25\%, 13≈33.3%\frac{1}{3} \approx 33.3\%, 15=20%\frac{1}{5} = 20\%.

Step 2: Profit-Loss Formulas

Master: Profit% = ProfitCP×100\frac{Profit}{CP} \times 100, SP = CP ×(1+P%100)\times (1 + \frac{P\%}{100}). Understand that profit/loss is always calculated on Cost Price.

Step 3: Interest Calculations

Know simple interest (SI=PRT100SI = \frac{PRT}{100}) and compound interest (A=P(1+R100)TA = P(1 + \frac{R}{100})^T). Class 8 students need compound interest mastery.

Step 4: Competition Practice

SparkEd's 60 curated Olympiad questions combine these concepts in competition-style problems.

Common Pitfalls

Common mistakes:

* Percentage base confusion — Percentage increase/decrease is always relative to the ORIGINAL value.
* Successive discount errors — Two 10% discounts is NOT 20% total. It is 1−(0.9)2=19%1 - (0.9)^2 = 19\%.
* Simple vs compound interest — Know the difference and when each applies.
* Profit on SP vs CP — Profit percentage is ALWAYS calculated on Cost Price unless stated otherwise.

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How Olympiad Papers Test This

SOF IMO tests through multi-step word problems combining percentages, profit-loss, and interest. IAIS focuses on real-world applications. Common formats: successive percentage changes, profit-loss with discount, and interest calculation word problems.

Practice Questions with Solutions

Try these!

Question 1: Successive Discounts

A shirt costs Rs. 800. Two successive discounts of 10% and 20% are offered. What is the final price?

Solution: After 10%: 800×0.9=720800 \times 0.9 = 720
After 20%: 720×0.8=576720 \times 0.8 = 576
Final price: Rs. 576

Question 2: Profit-Loss

A shopkeeper buys 10 pens at Rs. 8 each and sells them at Rs. 10 each. Find profit percentage.

Solution: CP = 10×8=8010 \times 8 = 80, SP = 10×10=10010 \times 10 = 100
Profit = 20, Profit% = 2080×100=25%\frac{20}{80} \times 100 = 25\%

Question 3: Compound Interest

Find compound interest on Rs. 10,000 at 10% for 2 years.

Solution: A=10000(1+10100)2=10000×1.21=12100A = 10000(1 + \frac{10}{100})^2 = 10000 \times 1.21 = 12100
CI = 12100−10000=210012100 - 10000 = 2100

How SparkEd Helps

SparkEd (sparkedmaths.com) offers 60 curated Olympiad-level Comparing Quantities questions for Class 7 and 8, with AI Spark Coach, unlimited worksheets, and multi-level difficulty. Completely free!

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Frequently Asked Questions

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