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Percentages show up everywhere a Class 8 student looks: sale signs, marks, bills, bank deposits. They are also where students lose marks for reasons that have nothing to do with arithmetic. The usual cause is taking the percentage of the wrong amount. This guide shows how to pick the right base every time, with worked examples for each kind of question.
Where is this topic in the 2026-27 NCERT books?
The older Class 8 chapter "Comparing Quantities" covered percentages, discounts, sales tax and GST, and compound interest. In the 2026-27 books the same ideas are in Ganita Prakash Grade 8 Part II, Chapter 1, "Fractions in Disguise". The title is the key idea: a percentage is a fraction with denominator 100. Ratios and proportion, which sit next to this, are in the chapters on proportional reasoning; see our guide to direct and inverse proportion.
Why compare with percentages at all?
"Fractions in Disguise" opens with a clear case. Eesha scored 42 out of 50 in English and 70 out of 80 in Science. Which was better? The maximum marks differ, so convert both:
English: 42 ÷ 50 × 100 = 84% Science: 70 ÷ 80 × 100 = 87.5%
Science was better, even though she lost more marks in it.
Which amount is the 100%?
The chapter shows why this matters. Manisha buys fertiliser at ₹500 a bag and sells it at ₹750. Her profit of ₹250 is 50% of her cost but only 33.33% of her selling price. Both numbers are correct; they answer different questions. In school problems, "profit per cent" means on the cost price unless the question says otherwise.
Worked examples: change, profit and discount
Percentage increase (from the chapter). Tomatoes cost ₹30 a kg three years ago and ₹42 now. Increase = ₹12. Percentage increase = 12 ÷ 30 × 100 = 40%.
Loss (from the chapter). A vase bought for ₹2,650 is sold at an 18% loss. Selling price = 82% of 2,650 = 0.82 × 2,650 = ₹2,173.
Successive discounts. A shop takes 20% off a ₹1,000 jacket, then a further 10% off at the till. Is that 30% off? After 20% off: 1,000 × 0.80 = ₹800. After a further 10%: 800 × 0.90 = ₹720. Total discount = ₹280, which is 28%, not 30%. The second discount is taken on ₹800, not on ₹1,000.
Working backwards from a price with GST. A bag costs ₹1,062 including 18% GST. What was the price before tax? Price with GST = 118% of the original. So original = 1,062 ÷ 1.18 = ₹900. Check: 18% of 900 = 162, and 900 + 162 = 1,062.
The common wrong answer is 1,062 × 0.82 = ₹870.84, which takes 18% off the wrong base. The older Class 8 chapter uses the same "start from ₹100" method: ₹100 becomes ₹112 with 12% GST, so divide by 1.12.
How do simple and compound interest differ?
"Fractions in Disguise" uses a fixed deposit of ₹6,000 at 10% per year for three years, with two options.
Option 1: interest paid out each year (simple interest). Each year the interest is 10% of ₹6,000 = ₹600. Over three years: ₹1,800 interest, so you receive ₹6,000 + ₹1,800 = ₹7,800 in all.
Option 2: interest added back each year (compound interest). Each year the whole amount grows by 10%, so multiply by 1.1 each year:
After year 1: 6,000 × 1.1 = ₹6,600
After year 2: 6,600 × 1.1 = ₹7,260
After year 3: 7,260 × 1.1 = ₹7,986
Compounding gives ₹186 more, because in years 2 and 3 you also earn interest on earlier interest. In one line: amount = P × (1 + r)ᵗ, with r as a decimal. Here, 6,000 × 1.1³ = 6,000 × 1.331 = ₹7,986.
One more. ₹10,000 at 8% a year for 2 years, compounded yearly. Amount = 10,000 × 1.08 × 1.08 = 10,000 × 1.1664 = ₹11,664. Compound interest = ₹1,664. Simple interest would be 2 × 800 = ₹1,600.
What mistakes should you avoid?
Wrong base. Discount on cost price, or profit on selling price, when the question means the other.
Adding successive percentages. 20% then 10% is 28%, not 30%. A 10% rise followed by a 10% fall leaves you at 99%, not 100%.
Undoing a percentage by subtracting it. To remove 18% GST, divide by 1.18.
Treating compound interest as simple. If the interest stays in the account, each year's interest is bigger than the last.
Writing "%" in the wrong place. 0.08 and 8% are the same; 0.08% is a hundred times smaller.
A practice routine
Name the base first. For every question, write "100% = ..." before calculating.
Three types a day: one percentage change, one profit-loss-discount, one interest.
Work backwards weekly: for each type, do one question where you are given the final amount and must find the original.
Use real bills. The chapter asks you to check the GST on bills at home. Do it, and check the arithmetic.
Getting a question wrong is useful if you study why; our post on how mistakes help learning explains how to use an error log. If you keep choosing the wrong base and cannot see why, the Fermi Problem Library has a step-by-step solver that explains the reasoning rather than printing an answer.
This week, take one bill from home and work out the price before GST from the total.
