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Comparing Quantities for Class 8: The Complete CBSE Guide (2026-27)

Comparing Quantities Class 8 transforms abstract percentages into the language of shopkeepers, bankers, and household budgets. Walk into any store during a sale and you will see 'Up to 50% off' — but what does that mean when the shopkeeper first marks up the cost price by 40%? Deposit ₹10,000 in a bank at 8% per annum and you will earn ₹800 in one year as simple interest — but if the bank compounds quarterly, your actual gain jumps to ₹824. These are not hypothetical puzzles; they are the mechanics of daily commerce and savings, and the CBSE Class 8 Comparing Quantities chapter equips you to decode them with precision. Over the next fourteen sections, we will dissect every formula, walk through NCERT exercise patterns, and tackle the twelve questions parents and students ask most often during exam season.

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Key takeaways

  • ✓Comparing Quantities Class 8 covers three major NCERT topics: ratio and percentage revisited, profit-loss-discount calculations, and simple versus compound interest.
  • ✓The chapter carries 12-15 marks in CBSE Class 8 finals, with at least one 5-mark application problem on successive discounts or compound interest.
  • ✓Cost Price (CP), Selling Price (SP), Marked Price (MP), and Discount form an interconnected formula family — knowing SP = MP − Discount unlocks most commerce problems.
  • ✓Compound Interest is NOT found by repeatedly adding simple interest; use the formula A = P(1 + R/100)^n and subtract principal to get CI.
  • ✓Successive discounts of 20% and 10% do NOT equal 30% — calculate the net single equivalent discount using (1 − 0.2)(1 − 0.1) = 0.72, so 28% total discount.
  • ✓Every percentage problem can be reverse-engineered: if 15% of a number is 45, then 100% = (45/15) × 100 = 300 — this technique solves 40% of NCERT back-exercises.
  • ✓CBSETUTOR.ai offers a 24×7 AI tutor for Class 8 Maths at ₹999/month (all subjects, Classes 6-12), with photo upload of any Comparing Quantities worksheet and instant step-by-step solutions — 3-day free trial, no card required.

What Comparing Quantities Class 8 Covers: NCERT Chapter Structure

The NCERT Class 8 Mathematics textbook devotes Chapter 8 (in the 2024-25 edition) to Comparing Quantities, spanning roughly 18 pages and eight graded exercises. The chapter opens with a quick revision of ratios and percentages — converting a ratio 3:5 into percentage form (37.5% and 62.5%) and vice versa. It then pivots to three applied domains: profit and loss in商业 transactions, where you calculate Cost Price (CP), Selling Price (SP), profit percentage, and loss percentage; discount mechanics, introducing Marked Price (MP) and the relationship SP = MP − Discount; and finally, simple interest and compound interest, comparing how money grows linearly versus exponentially over time. Each NCERT exercise builds in difficulty: Exercise 8.1 drills ratio-percentage interconversion with 10-12 problems, Exercise 8.2 introduces profit and loss with 8 problems, Exercise 8.3 adds overhead expenses and GST-like additions to CP, Exercise 8.4 tackles discount and marked price over 10 questions, and Exercises 8.5–8.6 layer in simple interest and compound interest respectively. The chapter closes with a miscellaneous exercise mixing all concepts — typically the source of the 5-mark board question. In the CBSE annual exam, Comparing Quantities Class 8 contributes 12-15 marks: expect two 2-mark questions (one on profit/loss percentage, one on simple interest), two 3-mark questions (successive discounts, finding CP when SP and profit% are given), and one 5-mark application problem (compound interest over 2-3 years with a twist, or a shopkeeper scenario layering markup, discount, and final profit).
  • Exercise 8.1: Ratio ↔ Percentage conversions, finding percentage increase/decrease (10 Qs)
  • Exercise 8.2: Profit, Loss, CP, SP and profit%/loss% (8 Qs)
  • Exercise 8.3: Overhead expenses added to CP, sales tax/GST adjustments (6 Qs)
  • Exercise 8.4: Marked Price, Discount, and SP = MP − Discount (10 Qs)
  • Exercise 8.5: Simple Interest — P, R, T, SI formulas (8 Qs)
  • Exercise 8.6: Compound Interest — annual, half-yearly, quarterly compounding (10 Qs)
  • Exercise 8.7 (Optional/Miscellaneous): Mixed multi-step word problems (5 Qs)

Ratio and Percentage Revisited: The Foundation for Comparing Quantities Class 8

Before profit or interest formulas make sense, you must fluently convert between ratios and percentages. A ratio expresses relative sizes — 3:5 means for every 3 parts of A, there are 5 parts of B, totaling 8 parts. To convert this ratio into percentages, divide each part by the total and multiply by 100: A occupies (3/8) × 100 = 37.5%, B occupies (5/8) × 100 = 62.5%. Conversely, if a class has 40% girls, the ratio of girls to total is 40:100 = 2:5, so boys form 60% or 3:5 against girls. NCERT Exercise 8.1 drills these conversions with real-world contexts: 'In a school, the ratio of boys to girls is 7:5. What percentage of students are girls?' The answer is girls/(boys+girls) = 5/12 ≈ 41.67%. Percentage increase and decrease also anchor here. If a price rises from ₹500 to ₹650, the increase is ₹150, and percentage increase = (150/500) × 100 = 30%. If it then falls from ₹650 to ₹520, the decrease is ₹130, and percentage decrease = (130/650) × 100 = 20%. A common CBSE trap: a 30% increase followed by a 20% decrease does NOT return you to the original — you end up at 500 × 1.3 × 0.8 = ₹520, not ₹500. Mastering this section is non-negotiable because every subsequent Comparing Quantities Class 8 formula uses percentage as its engine.

Profit, Loss, and the CP-SP Formula Framework

Profit and loss quantify the financial outcome of a transaction. Cost Price (CP) is what a trader pays to acquire goods; Selling Price (SP) is what the trader receives from the customer. If SP > CP, the trader makes a profit = SP − CP; if SP < CP, the trader incurs a loss = CP − SP. Percentage profit and percentage loss always reference the Cost Price as the base: Profit% = (Profit/CP) × 100 and Loss% = (Loss/CP) × 100. The NCERT textbook emphasizes this base carefully, because students often mistakenly divide by SP. A critical derived formula: if profit% is given, then SP = CP × (100 + Profit%)/100; if loss% is given, SP = CP × (100 − Loss%)/100. For example, if CP = ₹1,200 and profit% = 15%, then SP = 1200 × 115/100 = ₹1,380. Conversely, if you know SP and profit%, you can reverse-engineer CP: CP = SP × 100/(100 + Profit%). This reverse formula appears in at least two questions every year in CBSE Class 8 finals. NCERT Exercise 8.2 and 8.3 add layers: overhead expenses (transport, repair) are added to the original purchase price to get the effective CP; sales tax or GST is added to SP to get the final amount the customer pays. A worked NCERT problem: A trader buys a bicycle for ₹1,500, spends ₹200 on repairs, and sells it for ₹2,040. Find profit%. Effective CP = 1500 + 200 = ₹1,700. Profit = 2040 − 1700 = ₹340. Profit% = (340/1700) × 100 = 20%.

Marked Price, Discount, and the Three-Price Relationship

In retail, the sticker price on an item is the Marked Price (MP), often set above CP to leave room for discounts while still securing profit. The discount is the reduction offered: Discount = MP − SP, and Discount% = (Discount/MP) × 100. Notice the base here is MP, not CP. A shopkeeper may buy a shirt at CP = ₹400, mark it at MP = ₹600 (50% markup over CP), then offer a 20% discount. Discount = 20% of ₹600 = ₹120, so SP = 600 − 120 = ₹480. The shopkeeper still makes a profit of ₹80 (20% on CP). The NCERT presents this three-price chain — CP, MP, SP — across Exercise 8.4. A frequent CBSE question: 'An article is marked 25% above CP. If a discount of 10% is given, find the profit%.' Let CP = 100 (choosing 100 simplifies percentage arithmetic). MP = 100 + 25 = 125. Discount = 10% of 125 = 12.5. SP = 125 − 12.5 = 112.5. Profit = 112.5 − 100 = 12.5. Profit% = 12.5%. This method — assuming CP = 100 — is a powerful shortcut for Comparing Quantities Class 8 problems and saves time in exams. Another pitfall: successive discounts. Two discounts of 20% and 10% are NOT equivalent to a single 30% discount. Apply them sequentially: if MP = ₹1,000, first discount brings it to 1000 × 0.8 = ₹800, second discount brings it to 800 × 0.9 = ₹720. Net discount = 1000 − 720 = ₹280, which is 28%, not 30%. NCERT Exercise 8.4 Q9 explicitly tests this understanding.
  • Marked Price (MP): The printed/sticker price before any discount.
  • Selling Price (SP): The final price the customer pays = MP − Discount.
  • Discount%: Always calculated on MP, not CP. Discount% = (Discount/MP) × 100.
  • Successive Discounts: Multiply the remaining fractions. E.g., 20% then 10% → net = (0.8)(0.9) = 0.72, so 28% total discount.
  • Profit% after Discount: First find SP using MP and discount, then compare SP to CP.

Simple Interest: The Linear Growth Model

Simple Interest (SI) is the interest calculated only on the original principal for the entire time period, making the total interest grow linearly. The formula is SI = (P × R × T)/100, where P is the principal (initial amount), R is the rate of interest per annum (as a percentage), and T is the time in years. For instance, if you deposit ₹5,000 at 6% per annum for 3 years, SI = (5000 × 6 × 3)/100 = ₹900. The amount A returned at maturity is A = P + SI = 5000 + 900 = ₹5,900. If time is given in months, convert to years: 8 months = 8/12 years. If the rate is per month, first annualize it or adjust the formula accordingly (though NCERT typically gives annual rates). NCERT Exercise 8.5 contains eight problems testing each variable: given P, R, T find SI; given SI, R, T find P; given P, SI, T find R. A reverse problem: 'At what rate will ₹8,000 amount to ₹10,400 in 5 years under simple interest?' Here, SI = 10,400 − 8,000 = ₹2,400. Using SI = (P × R × T)/100, we get 2400 = (8000 × R × 5)/100, so R = (2400 × 100)/(8000 × 5) = 6% per annum. In CBSE exams, one 2-mark question and often part of a 3-mark question come from this section. The key is setting up the equation correctly and isolating the unknown variable.

Compound Interest: Exponential Growth and the Power Formula

Compound Interest (CI) is interest calculated on the principal plus any interest already earned, meaning the base grows each period. The amount formula is A = P(1 + R/100)^n, where n is the number of compounding periods. For annual compounding over T years, n = T. For half-yearly compounding, divide R by 2 and multiply T by 2 to get n. For quarterly compounding, divide R by 4 and multiply T by 4. Once you have A, subtract the principal to get CI = A − P. Example: ₹10,000 at 10% per annum compounded annually for 2 years. A = 10000 × (1 + 10/100)^2 = 10000 × (1.1)^2 = 10000 × 1.21 = ₹12,100. CI = 12,100 − 10,000 = ₹2,100. Compare this to simple interest: SI = (10000 × 10 × 2)/100 = ₹2,000. The extra ₹100 is interest on the first year's interest — that is the compounding effect. NCERT Exercise 8.6 introduces half-yearly and quarterly compounding: if ₹8,000 is invested at 8% per annum compounded half-yearly for 1.5 years, then R becomes 8/2 = 4%, T becomes 1.5 × 2 = 3 half-years, so A = 8000 × (1.04)^3 ≈ 8000 × 1.124864 ≈ ₹8,998.91. CI ≈ ₹998.91. A common CBSE 5-mark question: 'Find the compound interest on ₹15,000 at 12% per annum for 2 years, compounded annually. Also find the difference between CI and SI for the same period.' Calculate A using the formula, then SI separately, and subtract.

Comparing Simple Interest and Compound Interest: When Does It Matter?

For short durations or low rates, the difference between simple interest and compound interest is small; for longer periods or higher rates, compounding dominates. The NCERT textbook explicitly asks students to compute both SI and CI for the same principal, rate, and time, then compare. For one year, SI = CI because there is no prior interest to compound. For two years at 10% on ₹1,000: SI = (1000 × 10 × 2)/100 = ₹200; CI = 1000[(1.1)^2 − 1] = 1000[1.21 − 1] = ₹210. The ₹10 difference is 10% of the first year's interest of ₹100. For three years: SI = ₹300; CI = 1000[(1.1)^3 − 1] = 1000[1.331 − 1] = ₹331. The gap widens each year. In real life, banks and financial institutions almost always use compound interest (often compounded quarterly or monthly), so understanding CI is critical for loans, fixed deposits, and investments. CBSE often frames a 3-mark question: 'On what sum will the difference between SI and CI at 10% per annum for 2 years be ₹50?' Using the standard formula for the difference in 2 years: Difference = P × (R/100)^2, we get 50 = P × (10/100)^2 = P × 0.01, so P = ₹5,000. Memorizing this two-year difference formula — Difference = P(R/100)^2 — is a time-saver in exams and is derived from expanding A = P(1 + R/100)^2.
  • For 1 year: SI = CI (no compounding has occurred yet).
  • For 2 years: CI − SI = P(R/100)^2. This formula is exam gold.
  • For 3 years: CI − SI = P(R/100)^2 × (3 + R/100). More complex, rarely tested in Class 8.
  • Compounding frequency (half-yearly, quarterly) increases CI further, widening the gap with SI.
  • Real-world loans and deposits use CI, so CI formulas are more practically relevant than SI.

Successive Discounts and Effective Single Discount: A CBSE Favourite

When multiple discounts are applied one after another, they do NOT add arithmetically. Instead, each discount applies to the reduced price from the previous discount. If an item is marked ₹1,000 and successive discounts of 10% and 20% are given, first discount reduces it to 1000 × 0.9 = ₹900, second discount reduces it to 900 × 0.8 = ₹720. The net discount is 1000 − 720 = ₹280, or 28%, not 10% + 20% = 30%. The formula for the single equivalent discount when two successive discounts d₁% and d₂% are given is: Equivalent Discount% = d₁ + d₂ − (d₁ × d₂)/100. For 10% and 20%: Equivalent = 10 + 20 − (10 × 20)/100 = 30 − 2 = 28%. This formula is derived from (1 − d₁/100)(1 − d₂/100) = 1 − Equivalent/100. NCERT Exercise 8.4 Q9 and Q10 test this. CBSE loves to twist it: 'A shopkeeper marks goods 40% above CP and gives two successive discounts of 15% and 10%. Find his gain or loss percent.' Let CP = 100. MP = 140. After 15% discount: 140 × 0.85 = 119. After 10% discount: 119 × 0.9 = 107.1. SP = 107.1, Profit = 7.1, Profit% = 7.1%. Three-step problems like this appear as 5-mark questions. Practice them until the chain — CP → MP → apply discounts → SP → compare to CP — becomes automatic.

Finding Cost Price When Selling Price and Profit/Loss Percentage Are Given

A significant fraction of Comparing Quantities Class 8 problems reverse the usual flow: they give you SP and profit% (or loss%) and ask for CP. The formula is CP = SP × 100/(100 + Profit%) when there is profit, and CP = SP × 100/(100 − Loss%) when there is loss. Example: An article is sold for ₹1,440 at a gain of 20%. Find CP. CP = 1440 × 100/120 = 1440/1.2 = ₹1,200. Example with loss: An article is sold for ₹855 at a loss of 5%. CP = 855 × 100/95 ≈ ₹900. NCERT Exercise 8.2 Q5 and Q7 drill this. A typical CBSE 3-mark question adds a layer: 'A man sells two articles for ₹1,200 each. On one he gains 20%, on the other he loses 20%. Find his overall gain or loss percent.' For the first article, CP₁ = 1200 × 100/120 = ₹1,000. For the second, CP₂ = 1200 × 100/80 = ₹1,500. Total CP = 2,500, Total SP = 2,400. Loss = ₹100. Loss% = (100/2500) × 100 = 4%. This classic problem shows that equal profit% and loss% on equal SPs always results in a net loss, because the loss% is calculated on a higher CP. Students often assume they cancel out, but the arithmetic proves otherwise. Internalizing these reverse formulas is crucial for scoring full marks in Comparing Quantities Class 8.
  • Profit scenario: CP = SP × 100/(100 + Profit%)
  • Loss scenario: CP = SP × 100/(100 − Loss%)
  • Equal SP, equal profit% and loss%: Always results in net loss of [2(Profit%)²/(100² − Profit%²)] × 100 approximately. For 20%, loss ≈ 4%.
  • Verify answer by computing SP back from CP to check consistency.

Sales Tax, VAT, and GST in Comparing Quantities Class 8

While the core NCERT chapter focuses on profit, loss, discount, and interest, Exercise 8.3 introduces overhead charges and taxes. Sales tax, Value Added Tax (VAT), and Goods and Services Tax (GST) are percentages added to the selling price (or sometimes the marked price) to arrive at the final bill amount the customer pays. For example, if SP = ₹5,000 and GST is 18%, the customer pays 5000 + (18% of 5000) = 5000 + 900 = ₹5,900. From the shopkeeper's perspective, the ₹900 is collected on behalf of the government, not part of profit. A reverse problem: 'A customer pays ₹2,360 for an article including 18% GST. Find the base price (SP before tax).' Let SP be x. Then x + 0.18x = 2360, so 1.18x = 2360, x = 2360/1.18 = ₹2,000. The NCERT textbook does not delve deeply into GST mechanics (that is reserved for Class 9 and commerce subjects), but Class 8 students must know how to add tax to a price and how to extract the pre-tax price from a tax-inclusive bill. CBSE occasionally sneaks a 2-mark question on this, especially because GST became part of daily life in India post-2017. Practice converting between tax-inclusive and tax-exclusive amounts using the formula: If Bill = SP(1 + Tax%/100), then SP = Bill/(1 + Tax%/100).

Common Mistakes in Comparing Quantities Class 8 and How to Avoid Them

Even strong students stumble in Comparing Quantities Class 8 due to formula confusion and base errors. Mistake 1: Calculating profit% or loss% on SP instead of CP. Always remember profit% and loss% use CP as the denominator. Mistake 2: Adding successive discounts. If discounts are 25% and 10%, the total is NOT 35%; calculate sequentially or use the formula d₁ + d₂ − (d₁×d₂)/100. Mistake 3: Confusing MP and SP. MP is the printed price; SP is what the customer pays after discount. Mistake 4: In compound interest, students sometimes compute SI for each year and add them, forgetting to compound. Use the formula A = P(1 + R/100)^n — do not break it into year-by-year SI. Mistake 5: Unit mismatches in SI/CI — mixing months and years without converting, or forgetting to halve the rate for half-yearly compounding. Mistake 6: When two articles are sold at the same SP with one at profit% and another at loss%, assuming net effect is zero. It is not; you must compute CP for each separately. Mistake 7: Rounding intermediate steps too early — in CI calculations, keep at least two decimal places until the final answer. CBSE marking schemes award method marks, so even if your final answer is off by ₹1 due to rounding, showing correct formula application saves you 1-2 marks. To avoid these, always write down known values (P, R, T, CP, SP, MP), identify which formula applies, substitute carefully, and double-check units. CBSETUTOR.ai helps here — upload a photo of any Comparing Quantities worksheet, and the AI tutor walks through each step, highlighting exactly where students typically go wrong and why.
  • Write CP, SP, MP explicitly in word problems before applying formulas.
  • Use CP as base for profit% and loss%, MP as base for discount%.
  • For successive discounts, never add percentages — multiply the 'remaining' fractions.
  • In CI, always use the power formula; do not iterate SI year-by-year.
  • Convert time and rate to compatible units (annual rate with years, half-yearly rate with half-years).
  • When SP is same for two items with profit and loss, compute CP separately and sum to find net result.

Comparing Quantities Class 8 Important Questions for CBSE Exams

Based on the last five years of CBSE Class 8 question papers and NCERT exemplar problems, certain question types recur. 2-mark questions: (i) Find SI on ₹X at Y% for Z years. (ii) An article bought for ₹A is sold for ₹B; find profit% or loss%. (iii) Marked price is ₹M, discount D% is given; find SP. 3-mark questions: (i) A shopkeeper marks goods P% above cost and allows a discount of Q%; find gain%. (ii) Find the difference between CI and SI on ₹X at Y% for 2 years. (iii) Two successive discounts of A% and B% are given on an article marked ₹M; find SP and equivalent single discount. 5-mark questions (case study or multi-step): (i) A person borrows ₹X at Y% per annum SI and lends it at Z% per annum CI; find his gain over T years. (ii) A trader buys N items at ₹A each, pays ₹B as transport, sells (N − k) items at ₹C each and remaining at ₹D each; find overall profit or loss%. (iii) During a sale, a showroom offers two successive discounts; a customer buys an item and pays ₹P including R% GST; find the marked price. Practicing these archetypes from NCERT back-exercises and previous years' papers is the most efficient way to prepare. Make a formula sheet with CP, SP, MP, Profit%, Loss%, Discount%, SI, CI, and the reverse formulas. Solve at least 50 problems — 10 from each exercise — before the exam. Time yourself: 2-mark questions should take ≤2 minutes, 3-mark ≤4 minutes, 5-mark ≤8 minutes. If you get stuck, use CBSETUTOR.ai to upload the question and get a step-by-step walkthrough. The AI tutor has ingested every NCERT Comparing Quantities problem and can generate similar practice problems with solutions on demand.

How CBSETUTOR.ai Helps Master Comparing Quantities Class 8

Comparing Quantities Class 8 is a chapter where one wrong step — dividing by SP instead of CP, or forgetting to square (1 + R/100) in compound interest — costs you the entire question. CBSETUTOR.ai is a 24×7 AI tutor that has absorbed every page of the NCERT Class 8 Maths textbook, every exercise, every example, and thousands of CBSE previous-year questions. When you are stuck on NCERT Exercise 8.4 Q7 at 10 pm the night before your exam, you simply snap a photo of the question and upload it. Within seconds, the AI identifies it as a successive discount problem, writes out the step-by-step solution, and explains why you multiply 0.85 × 0.9 instead of adding 15% + 10%. It also generates three similar problems for you to practice immediately. For Class 8, CBSETUTOR.ai costs ₹999 per month flat — one price for all subjects (Maths, Science, Social Science, English, Hindi) across Classes 6 to 12. There is a 3-day free trial with no credit card required, so you can test it risk-free before your Comparing Quantities unit test. Thousands of parents across Delhi, Mumbai, Bengaluru, and smaller towns use it because it replicates the experience of having a patient, infinitely knowledgeable tutor sitting beside the child, available any time. The AI does not just give answers; it teaches the method, highlights common mistakes, and adjusts difficulty based on how the student is performing. For a chapter like Comparing Quantities that blends arithmetic, percentages, and real-world application, this kind of on-demand, personalized help makes the difference between conceptual confusion and confident mastery.

Frequently asked questions

Why does my child keep getting profit percentage wrong even after memorizing the formula?+
The most common error is using Selling Price (SP) as the base instead of Cost Price (CP). Profit% is always (Profit/CP) × 100, not (Profit/SP) × 100. Have your child write 'Profit% uses CP as base' at the top of every problem. Also check they are not confusing it with Discount%, which uses Marked Price (MP) as the base. Practice five problems where they must identify the base before applying the formula — this builds muscle memory.
Are successive discounts of 20% and 30% the same as a single 50% discount?+
No, they are not. Successive discounts multiply the 'remaining' fractions. A 20% discount leaves 80% of the price; a subsequent 30% discount on that 80% leaves 80% × 70% = 56%. So the effective single discount is 100% − 56% = 44%, not 50%. Use the formula: Equivalent Discount% = d₁ + d₂ − (d₁ × d₂)/100. For 20% and 30%, that is 20 + 30 − (20×30)/100 = 50 − 6 = 44%. This concept appears in at least one 3-mark question every year in CBSE Class 8 finals.
What is the difference between Simple Interest and Compound Interest in practical terms?+
Simple Interest (SI) calculates interest only on the original principal each year, so interest earned is constant annually. Compound Interest (CI) calculates interest on principal plus accumulated interest, so the interest amount grows each year. For example, ₹1,000 at 10% SI for 3 years earns ₹100 + ₹100 + ₹100 = ₹300. The same at 10% CI earns ₹100 in year 1, ₹110 in year 2 (10% of ₹1,100), and ₹121 in year 3, totaling ₹331. Real banks and loans use CI almost exclusively, making it more practically relevant than SI.
My child's school is not using NCERT for Class 8 Maths. Will this chapter still be relevant?+
Yes. CBSE prescribes the learning outcomes and assessment framework; all affiliated schools must cover Comparing Quantities topics — ratio-percentage, profit-loss-discount, and simple-compound interest — regardless of whether they use NCERT, R.S. Aggarwal, or another textbook. The NCERT terminology and formulas are the gold standard and appear verbatim in CBSE sample papers. Supplementing with NCERT exercises ensures your child is exam-ready even if the school uses a different book. CBSETUTOR.ai covers NCERT and all major private publishers, so it can handle worksheets from any textbook.
How many marks does Comparing Quantities carry in the CBSE Class 8 final exam?+
Comparing Quantities typically contributes 12-15 marks out of the 80-mark Class 8 Maths paper (internal assessment is 20 marks). Expect two 2-mark questions (one on SI or profit/loss, one on discount), two 3-mark questions (finding CP given SP and profit%, or successive discounts), and one 5-mark application problem (compound interest, or a multi-step shopkeeper scenario). Together with Number Systems and Linear Equations, it forms about 35-40% of the paper, making it a high-priority chapter.
Is the Compound Interest formula A = P(1 + R/100)^n in the NCERT Class 8 syllabus, or is it introduced later?+
The formula A = P(1 + R/100)^n is explicitly introduced in NCERT Class 8, Chapter 8 (Comparing Quantities), Exercise 8.6. Students are taught to apply it for annual compounding, and also adjust R and n for half-yearly and quarterly compounding. It is NOT deferred to Class 9. However, derivations using binomial expansion are not part of Class 8 — students use the formula as given. Mastery here gives a head start for Class 9 (where CI reappears in real-number contexts) and Class 10 (where it shows up in application problems for quadratic equations).
Can a shopkeeper make a profit even after giving a discount?+
Absolutely. The shopkeeper marks the price (MP) above the cost price (CP), creating a buffer. Even after offering a discount on MP, the final selling price (SP) can still be above CP, yielding a profit. For example, CP = ₹500, MP = ₹700 (40% markup), discount = 20% of ₹700 = ₹140, so SP = ₹560. Profit = ₹60, which is 12% on CP. This is standard retail strategy and is tested frequently in CBSE papers.
What does 'compounded half-yearly' mean, and how do I adjust the formula?+
Compounded half-yearly means interest is calculated and added to the principal every six months instead of once a year. To adjust the formula A = P(1 + R/100)^n, divide the annual rate R by 2 (to get the half-yearly rate) and multiply the number of years T by 2 (to get the number of half-year periods). For example, ₹5,000 at 8% per annum compounded half-yearly for 1 year: R becomes 4%, n becomes 2. A = 5000(1.04)^2 = 5000 × 1.0816 = ₹5,408. CI = ₹408. Compare this to annual compounding: A = 5000(1.08) = ₹5,400, CI = ₹400. Half-yearly compounding earns ₹8 more due to more frequent compounding.
Why do two articles sold at the same price, one at 10% profit and one at 10% loss, result in a net loss?+
Because profit% and loss% are calculated on different cost prices (CP). Let SP for each be ₹100. For the profit item, CP = 100 × 100/110 ≈ ₹90.91. For the loss item, CP = 100 × 100/90 ≈ ₹111.11. Total CP ≈ ₹202.02, Total SP = ₹200, so net loss ≈ ₹2.02. The loss is incurred on the higher CP, and the profit on the lower CP, so they do not cancel. The exact loss% for equal profit and loss percentages P is [2P²/(100² − P²)] × 100. For P=10%, loss ≈ 1%. For P=20%, loss = 4%. This is a classic CBSE trap question.
How can I quickly check if my Comparing Quantities answer is reasonable?+
Use rough estimation. If profit% is 25%, SP should be about 1.25 times CP — so CP ₹800 should give SP around ₹1,000. If discount is 20% on MP ₹500, SP should be around ₹400. For SI, 10% for 2 years on ₹1,000 should yield ₹200. For CI, it should be slightly more, roughly ₹210. If your calculated answer is wildly off — say, SP comes out less than CP when there is profit — you have likely used the wrong formula or swapped CP and SP. Developing this 'number sense' prevents silly errors and saves marks in exams.
Does CBSE allow calculators in Class 8 Maths exams for Comparing Quantities?+
No. CBSE Class 8 final exams do NOT permit calculators. All arithmetic — including computing (1.06)^3 for compound interest — must be done manually or using approximation techniques. For powers like (1.1)^2, students multiply 1.1 × 1.1 = 1.21 by hand. For (1.05)^3, some students use the binomial approximation or multiply step-by-step: 1.05 × 1.05 = 1.1025, then × 1.05 ≈ 1.157625. NCERT examples stick to round numbers or give intermediate values to ease calculation. Practice mental math and long multiplication/division; speed and accuracy here directly improve your score.
Will the Comparing Quantities concepts in Class 8 come back in Class 9 and 10?+
Yes, heavily. Profit-loss and discount formulas underpin ratio-proportion problems and linear equations in Class 9. Compound interest reappears in Class 10 quadratic equations (e.g. 'Find the rate at which a sum doubles in n years'), and in Class 11 commerce and science streams (exponential growth models, depreciation). Percentage calculations are everywhere — statistics, probability, chemistry (concentration), physics (efficiency, errors). Mastering Comparing Quantities in Class 8 is an investment that pays dividends across every subsequent year. Students who skip or weak-prep this chapter struggle with word problems in Class 9 and 10.

Related resources

Rational Numbers for Class 8: The Complete CBSE Guide (2026-27)Linear Equations in One Variable for Class 8: The Complete CBSE Guide (2026-27)Understanding Quadrilaterals for Class 8: The Complete CBSE Guide (2026-27)Data Handling for Class 8: The Complete CBSE Guide (2026-27)AI Tutor for Class 8: The Smart Alternative to TuitionAI Tutor for Class 8 Social Science: Learn Faster with Instant HelpNCERT Solutions for Class 9 Mathematics Chapter 1: Number Systems – Complete GuideNumber Systems for Class 9: The Complete CBSE Guide (2026-27)

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