Comparing Quantities for Math Olympiad: Complete Preparation Guide

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

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 $1 - (0.9)^2 = 19\%$.
• 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.

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%: $800 \times 0.9 = 720$
After 20%: $720 \times 0.8 = 576$
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 = $10 \times 8 = 80$, SP = $10 \times 10 = 100$
Profit = 20, Profit% = $\frac{20}{80} \times 100 = 25\%$

Question 3: Compound Interest

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

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

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