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CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages — Notes

CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages is one of the most practical chapters in the entire NCERT Class 7 Mathematics curriculum. Whether you are calculating the discount on a new pair of shoes, figuring out how much interest your savings account earns, or scaling a recipe from four servings to ten, you are using ratios, proportions, and percentages. This chapter teaches you three interlinked tools for comparing and working with quantities: ratios let you compare two numbers in simplest form, proportions help you find unknown values when two ratios are equal, and percentages express parts of a whole on a universal 0-100 scale. Building on these foundations, the chapter then introduces profit, loss, and simple interest — real financial calculations every student and parent encounters. These notes cover every concept from the 2024-25 NCERT textbook with worked examples, formula derivations, and common-error warnings to help you master CBSE Class 7 Mathematics Chapter 10.

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Key takeaways

  • ✓A ratio is a comparison of two like quantities and must always be simplified by dividing both terms by their HCF to reach simplest form.
  • ✓In any proportion a: b = c: d, the cross-multiplication rule a × d = b × c lets you solve for any one unknown term when three are known.
  • ✓Percentage means per hundred; convert to fraction (÷100) before multiplying, and always multiply a fraction by 100 to express it as a percentage.
  • ✓Profit % and Loss % are always calculated on Cost Price (CP), never on Selling Price: Profit % = (Profit ÷ CP) × 100.
  • ✓Simple Interest is calculated using SI = (P × R × T) ÷ 100, where P is principal, R is annual rate in %, and T is time in years; Amount = P + SI.
  • ✓Direct proportion means both quantities increase or decrease together in the same ratio, a pattern seen in cost-quantity and distance-time problems.
  • ✓Real-world applications of CBSE Class 7 Mathematics Chapter 10 include shopping discounts, bank interest, recipe scaling, and comparing test scores across classes.

Understanding Ratios and Simplification

A ratio compares two quantities of the same kind. When you say the ratio of boys to girls in your class is 3:2, you mean that for every 3 boys there are 2 girls. Ratios are written as a: b and are read as 'a to b'. The two numbers are called the terms of the ratio; the first term is the quantity being compared, and the second term is the quantity it is being compared to. Why does this matter in CBSE Class 7 Mathematics Chapter 10? Because ratios help us understand relative sizes without needing exact counts. A baker might specify that the ratio of flour to sugar is 5:2, which tells you the balance of ingredients whether you make one cake or a hundred. Just like fractions, every ratio must be simplified to its simplest form by dividing both terms by their Highest Common Factor (HCF). For instance, the ratio 12:8 has HCF 4, so it simplifies to 3:2. Similarly, 50:100 simplifies to 1:2 because HCF is 50. A ratio is in simplest form when the HCF of both terms is 1. Consider a school with 60 footballs and 40 basketballs: the ratio 60:40 simplifies to 3:2 (HCF = 20), telling you that for every 3 footballs there are 2 basketballs. You can also express ratios as fractions: the ratio 3:2 means the first quantity represents 3/5 of the total and the second represents 2/5, since 3 + 2 = 5 parts total. This dual representation — as a ratio or a fraction — is a core skill in CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages and appears frequently in board-aligned worksheets and NCERT exercises.
  • A ratio a:b compares two quantities; both must have the same unit (e.g., both in kg or both in rupees).
  • Simplest form is reached by dividing both terms by their HCF; for 18:24, HCF = 6, so simplest form is 3:4.
  • Ratios can be written as fractions: 3:2 is equivalent to 3/5 for the first part and 2/5 for the second part of the total.
  • Real-life uses include ingredient proportions in recipes, comparing speeds, and analyzing class demographics.

Proportions and the Cross-Multiplication Rule

A proportion is a statement that two ratios are equal. If a: b = c: d, we say 'a is to b as c is to d' and call this a proportion. The terms a and d are the extremes (outer terms), while b and c are the means (inner terms). The fundamental rule governing proportions in CBSE Class 7 Mathematics Chapter 10 is that the product of the means equals the product of the extremes: a × d = b × c. This cross-multiplication rule is your superpower for solving proportion problems. If you know any three of the four terms, you can always find the fourth. Consider a real example from the NCERT: if 5 notebooks cost ₹150, how much do 12 notebooks cost? Set up the proportion 5 notebooks: ₹150 = 12 notebooks: x rupees, which translates to 5/150 = 12/x. Cross-multiplying gives 5 × x = 150 × 12, so x = 1800 ÷ 5 = ₹360. This type of problem is called direct proportion: as one quantity increases, the other increases in the same ratio. There is also inverse proportion (covered in later classes), where an increase in one quantity causes a proportional decrease in the other, such as the relationship between speed and time for a fixed distance. Mastery of cross-multiplication in CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages is essential because it appears in word problems involving cost-quantity, distance-time, and work-rate scenarios. Always write the proportion carefully, label your terms, and double-check that the product of extremes equals the product of means before solving.

Percentages — Meaning, Conversions, and Applications

The word percentage literally means 'per hundred'. A percentage is a ratio expressed as a fraction with denominator 100, and the symbol is %. So 25% means 25/100, which simplifies to 1/4; 50% means 50/100 or 1/2; and 100% means 100/100 or 1 (the whole). Why use percentages in CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages? They provide a universal scale to compare parts across different totals. If 30 students in Class A and 25 students in Class B scored above 80%, you cannot immediately compare performance unless you know each class size. Percentages normalise the comparison. You must be fluent in four conversions: (1) Percentage to Decimal — divide by 100, so 35% = 0.35. (2) Decimal to Percentage — multiply by 100, so 0.72 = 72%. (3) Percentage to Fraction — write over 100 and simplify, so 40% = 40/100 = 2/5. (4) Fraction to Percentage — multiply by 100, so 3/5 = (3/5) × 100 = 60%. A typical NCERT Class 7 Mathematics problem: a shirt costs ₹800 and is given a 20% discount; find the discount amount. Discount = 20% of 800 = (20/100) × 800 = 0.2 × 800 = ₹160, so the new price is 800 − 160 = ₹640. Notice that you always convert the percentage to a fraction or decimal before performing the multiplication. Forgetting this step is the most common error in CBSE Class 7 Mathematics Chapter 10.
  • Percentage = (Part/Whole) × 100; it expresses how many parts out of every hundred.
  • To find x% of a number N, compute (x/100) × N or 0.0x × N after converting to decimal.
  • Conversions: 25% = 0.25 = 1/4; 75% = 0.75 = 3/4; memorise these common equivalences for speed.
  • Real uses: discounts in shops (20% off), test scores (scored 85%), interest rates (8% per annum).

Calculating Profit, Loss, and Their Percentages

When a shopkeeper buys an item for one price and sells it for another, the difference is either profit or loss. Cost Price (CP) is the price at which something is bought; Selling Price (SP) is the price at which it is sold. If SP > CP, there is a Profit = SP − CP. If SP < CP, there is a Loss = CP − SP. However, in CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages, profit and loss are almost always expressed as percentages of the Cost Price so you can compare deals across items of different values. The formulae are Profit % = (Profit ÷ CP) × 100 and Loss % = (Loss ÷ CP) × 100. Notice that the denominator is always CP, never SP. This is crucial. For example, a fruit seller buys apples at ₹40 per kg and sells them at ₹50 per kg. CP = ₹40, SP = ₹50, so Profit = 50 − 40 = ₹10. Profit % = (10 ÷ 40) × 100 = 25%. In another scenario, a book costs ₹200 to print but is sold for ₹160. CP = ₹200, SP = ₹160, so Loss = 200 − 160 = ₹40. Loss % = (40 ÷ 200) × 100 = 20%. These calculations appear in almost every NCERT Class 7 Mathematics exercise on this topic and are a staple of school tests. Always identify CP and SP first, compute the absolute profit or loss, then convert to percentage using CP as the base. A common student error is using SP in the denominator; this yields an incorrect percentage and will cost marks in exams.

Simple Interest — Formula and Step-by-Step Calculation

When you borrow or lend money, the interest is the extra amount paid for the use of that money. Simple Interest (SI) is interest calculated only on the original sum, called the Principal (P), and not on any accumulated interest. The NCERT formula taught in CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages is SI = (P × R × T) ÷ 100, where P is the principal in rupees, R is the rate of interest per annum (per year) expressed as a percentage, and T is the time in years. The Amount (A) you receive or repay is the sum of principal and interest: A = P + SI. Consider an NCERT example: you deposit ₹5000 in a bank at 8% per annum for 3 years. P = 5000, R = 8, T = 3. Compute SI = (5000 × 8 × 3) ÷ 100 = 120000 ÷ 100 = ₹1200. Amount = 5000 + 1200 = ₹6200. So after 3 years, your ₹5000 grows to ₹6200. Another example: a loan of ₹2000 at 6% per annum for 2 years yields SI = (2000 × 6 × 2) ÷ 100 = 24000 ÷ 100 = ₹240, and Amount = 2000 + 240 = ₹2240. Simple interest is used by many banks, microfinance institutions, and in short-term loans. It is simpler than compound interest (which you will study in Class 8) because it does not compute interest on previously earned interest. When solving SI problems in CBSE Class 7 Mathematics Chapter 10, always write down P, R, and T explicitly, substitute into the formula, and show every multiplication and division step to avoid arithmetic errors.

Worked Example — Combining Ratios, Proportions, and Percentages

Let us solve a multi-part problem typical of CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages. Question: In a school, the ratio of boys to girls is 5:3. There are 250 boys. (a) How many girls are there? (b) If every 5 students require 2 notebooks, how many notebooks are needed for all students? Solution Part A — Finding the number of girls: Ratio boys:girls = 5:3. Number of boys = 250. Let number of girls = x. Set up proportion 5:3 = 250:x, which means 5/3 = 250/x. Cross-multiply: 5 × x = 3 × 250 → 5x = 750 → x = 750 ÷ 5 = 150. Answer: 150 girls. Part B — Finding notebooks needed: Total students = 250 + 150 = 400. Ratio students:notebooks = 5:2. If 5 students need 2 notebooks, then 400 students need y notebooks. Proportion: 5:2 = 400:y → 5/2 = 400/y. Cross-multiply: 5 × y = 2 × 400 → 5y = 800 → y = 160. Answer: 160 notebooks. This example shows how proportion solves for unknowns efficiently and how ratio reasoning extends to real resource-allocation problems. Notice that we simplified each step, labelled every variable, and verified that our proportion was set up correctly before cross-multiplying.
  • Always identify what quantities are being compared and set up the ratio or proportion with correct labels (boys, girls, notebooks, etc.).
  • Cross-multiplication is valid only when you have a true proportion (two equal ratios); do not apply it to inequalities.
  • After finding an answer, do a quick sanity check: does 150 girls fit the 5:3 ratio with 250 boys? Yes, because 250:150 simplifies to 5:3.

Worked Example — Profit, Loss, and Simple Interest Combined

Here is a comprehensive problem integrating profit-loss and simple interest from CBSE Class 7 Mathematics Chapter 10. Question: A shopkeeper buys a dozen pens for ₹360. He sells each pen for ₹35. Find (a) his profit per pen and profit %, (b) if he invests his total profit in a bank at 10% per annum for 2 years, how much interest does he earn? Solution Part A — Profit calculation: Cost price of 12 pens = ₹360, so cost price per pen = 360 ÷ 12 = ₹30. Selling price per pen = ₹35. Profit per pen = 35 − 30 = ₹5. Profit % = (Profit ÷ CP) × 100 = (5 ÷ 30) × 100 = 500 ÷ 30 = 16.67% (or exactly 50/3 %). Answer: Profit per pen = ₹5; Profit % ≈ 16.67%. Part B — Simple interest on total profit: Total profit for 12 pens = 5 × 12 = ₹60. Principal P = ₹60, Rate R = 10% per annum, Time T = 2 years. SI = (P × R × T) ÷ 100 = (60 × 10 × 2) ÷ 100 = 1200 ÷ 100 = ₹12. Amount = P + SI = 60 + 12 = ₹72. Answer: Interest earned = ₹12; Total amount after 2 years = ₹72. This problem is a favourite in NCERT Class 7 Mathematics exercises because it tests whether you can chain two concepts — first compute profit %, then use that profit as principal for SI. Each step must be shown clearly in exams to earn full marks.

Key Formulas Summary for Quick Revision

CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages contains several core formulas that you must memorise and apply correctly. For ratios: Simplest form is obtained by dividing both terms by their HCF. For proportions: If a:b = c:d, then a × d = b × c (cross-multiplication rule). For percentages: Percentage of a number = (Percentage ÷ 100) × Number. For example, 15% of 200 = (15 ÷ 100) × 200 = 30. For profit and loss: Profit % = (Profit ÷ CP) × 100 and Loss % = (Loss ÷ CP) × 100. Remember that the denominator is always Cost Price. For simple interest: SI = (P × R × T) ÷ 100, where P = principal, R = rate per annum (%), T = time in years. The total Amount = P + SI. Additionally, you can rearrange the SI formula to find any one variable if the other three are known. For instance, if SI, R, and T are given, then P = (SI × 100) ÷ (R × T). These rearrangements are occasionally tested in NCERT exercises and school exams. Make sure you understand the logic behind each formula rather than rote-memorising it; this understanding will help you adapt to word problems that present information in varied formats.
  • Simplify ratios: divide both terms by HCF. Example: 18:24 → HCF = 6 → 3:4.
  • Proportion: a:b = c:d implies a × d = b × c. Solve for unknown by isolating it after cross-multiplication.
  • Percentage to decimal: divide by 100. Decimal to percentage: multiply by 100.
  • Profit % = (Profit ÷ CP) × 100. Loss % = (Loss ÷ CP) × 100. Always use CP as denominator.
  • SI = (P × R × T) ÷ 100. Amount = P + SI. Rearrange for P, R, or T if needed.

Common Mistakes and How to Avoid Them

Students preparing for CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages often make predictable errors. Mistake 1: Writing 15% as 15 in calculations instead of 15/100 or 0.15. Always convert the percentage to a fraction or decimal before multiplying. Mistake 2: Calculating profit % or loss % using Selling Price in the denominator instead of Cost Price. The correct denominators are always CP: Profit % = (Profit ÷ CP) × 100 and Loss % = (Loss ÷ CP) × 100. Mistake 3: Forgetting to simplify ratios. Leaving an answer as 20:30 instead of 2:3 will lose marks because the question asks for simplest form. Always find the HCF and divide. Mistake 4: Mixing up extremes and means in proportions. In a:b = c:d, the extremes are a and d, the means are b and c. Cross-multiplication gives a × d = b × c, not a × b = c × d. Mistake 5: Using the wrong time unit in simple interest. If the rate is per annum and time is given in months, convert months to years by dividing by 12. For instance, 6 months = 6/12 = 0.5 years. Mistake 6: Misreading 'profit on CP' versus 'markup on SP' in word problems. NCERT consistently uses profit and loss relative to CP; be alert if a problem asks for markup or discount relative to marked price, which is a variant introduced in later classes. Mistake 7: Arithmetic slips when cross-multiplying large numbers. Always show intermediate steps and double-check your multiplication and division. These errors are avoidable through careful reading, systematic working, and practice with NCERT Class 7 Mathematics exercise problems.
  • Convert percentage to 0.0x or x/100 before any multiplication; never use the raw percentage number.
  • Profit % and Loss % denominators are always CP, never SP. Write the formula before substituting to avoid confusion.
  • Simplify every ratio to HCF = 1 form before writing your final answer.
  • In SI formula, ensure time T is in years; convert months or days if necessary.
  • Cross-multiplication: a:b = c:d means a×d = b×c. Do not swap the products.

Real-World Applications of Ratios, Proportions, and Percentages

Why does CBSE include Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages in the curriculum? Because these concepts appear daily in the real world. Ratios are used in recipes (2 cups flour: 1 cup sugar), in maps (scale 1:50000 means 1 cm on the map = 50000 cm on the ground), and in mixing paint colours (3 parts blue: 1 part yellow for green). Proportions solve questions like 'If 8 workers build a wall in 5 days, how long will 10 workers take?' (inverse proportion) or 'If 3 kg of rice costs ₹180, what is the cost of 7 kg?' (direct proportion). Percentages dominate finance and commerce: shop discounts (Flat 25% off!), sales tax (GST is 18%), interest on savings (earn 4% per annum), inflation rates (prices rose 6% last year), and test scores (you scored 88% in mathematics). Simple interest is used by banks for fixed deposits, by microfinance for small loans, and in many government schemes. Understanding these tools empowers you to make informed decisions: Is a 20% discount better than a flat ₹200 off? How much will your ₹5000 birthday gift grow to in a 5-year RD at 7% SI? If a shopkeeper marks up cost price by 30% and then gives a 10% discount, do you pay more or less than CP? CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages builds the quantitative literacy every citizen needs in a modern economy.

Linking Chapter 10 to Other NCERT Class 7 Mathematics Topics

CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages does not exist in isolation; it connects to multiple other chapters. Chapter 1 Integers and Chapter 2 Fractions and Decimals provide the arithmetic foundation — you cannot simplify ratios or compute percentages without fluency in HCF, LCM, and fraction operations. Chapter 8 Comparing Quantities (in some NCERT editions this is merged with Chapter 10) extends profit-loss and discount problems to concepts like marked price, overhead expenses, and sales tax, building on the CP-SP framework you learn here. Chapter 11 Algebraic Expressions introduces variables, and many proportion problems can be set up as simple linear equations (if 5x = 3y, find the ratio x:y). Chapter 13 Exponents and Powers will later help you understand compound interest (Class 8), which iteratively applies percentage increases. Even Chapter 3 Data Handling uses percentages to interpret pie charts and compare survey results. The idea of 'per hundred' is universal. When you progress to Class 8, you will revisit these topics in Comparing Quantities with more complexity (successive discounts, compound interest, profit-loss with GST). The habit of setting up proportions correctly and converting between fractions, decimals, and percentages fluently will save you significant time in higher classes and in competitive exams like NTSE and Olympiads. Treat CBSE Class 7 Mathematics Chapter 10 as a foundational pillar for financial mathematics and real-world problem-solving.
  • Integers and fractions (Chapters 1, 2) enable you to simplify ratios and perform percentage calculations.
  • Algebraic thinking (Chapter 11) lets you express proportions as equations and solve for unknowns symbolically.
  • Data handling (Chapter 13) uses percentages to present survey data, pie charts, and comparative statistics.
  • Class 8 Comparing Quantities builds on Chapter 10 by adding compound interest, successive discounts, and tax calculations.

How CBSETUTOR.ai Helps You Master Chapter 10

Many Class 7 students find word problems in CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages challenging because they require translating sentences into mathematical setups. Should I use a proportion or a percentage calculation? Is this profit or loss? Is the time in years or months? CBSETUTOR.ai offers a 24×7 AI tutor that has ingested every page of the NCERT Class 7 Mathematics textbook, including all worked examples, exercise problems, and common variations. When you are stuck on a homework question — say, Exercise 10.2 Question 5 — you can upload a photo of the problem, and the AI will guide you step-by-step: it will show you how to identify CP and SP, set up the profit formula, and compute the percentage, explaining each line in simple language. If you make an error (like using SP instead of CP in the denominator), the tutor will catch it and explain why that is wrong, helping you build the correct mental model. You can ask follow-up questions in natural language: 'Why do we always divide by CP?' or 'What if the problem gives profit % and SP, how do I find CP?' The AI will provide worked examples and practice problems tailored to your doubt. The entire NCERT syllabus for Classes 6–12 is covered, so your younger sibling in Class 6 and your older sibling in Class 10 can use the same subscription. The cost is a flat ₹999 per month — one price for all classes, with a 3-day free trial and no credit card required to start. Parents across India use CBSETUTOR.ai to give their children on-demand homework help and concept clarity without the expense and scheduling rigidity of traditional tuitions.
  • Upload a photo of any NCERT exercise question and get instant, step-by-step guidance aligned to CBSE Class 7 Mathematics Chapter 10.
  • Ask 'Why do we use CP and not SP in profit %?' and receive a clear explanation with examples, available 24×7.
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Exam Strategy and Scoring Tips for Chapter 10

CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages typically carries 12–15 marks in the annual exam, distributed across 2-mark, 3-mark, and occasionally 5-mark word problems. Here is how to maximise your score. Tip 1: In ratio and proportion problems, always write the ratio in simplest form and show the HCF calculation; examiners award a mark for simplification. Tip 2: When solving proportions, set up the equation clearly, show the cross-multiplication step, and solve for the unknown algebraically. Even if your final answer is wrong due to an arithmetic slip, you can earn partial marks for correct method. Tip 3: For percentage problems, convert the percentage to a fraction or decimal in the first line of your solution; this demonstrates understanding and prevents errors. Tip 4: In profit-loss questions, always write CP =..., SP =..., Profit = SP − CP (or Loss = CP − SP), then Profit % = (Profit ÷ CP) × 100. This structured approach ensures you do not mix up the values. Tip 5: For simple interest, write P, R, T explicitly, substitute into SI = (P × R × T) ÷ 100, and show the arithmetic. Finally, write Amount = P + SI. Examiners look for these steps. Tip 6: Underline or box your final answer so it is easy to spot. Tip 7: Attempt all questions; even if you cannot complete a 5-mark problem, write the relevant formula and any partial work for 1–2 marks. Tip 8: Practice previous years' CBSE question papers; profit-loss and SI problems repeat in structure. Time management is crucial: allocate about 2 minutes per mark, so a 3-mark question should take roughly 6 minutes. With disciplined practice of NCERT exercises and sample papers, a score of 12+ out of 15 is very achievable in CBSE Class 7 Mathematics Chapter 10.
  • Show all intermediate steps: HCF for ratios, cross-multiplication for proportions, formula substitution for SI.
  • Write CP, SP, Profit, and Profit % on separate lines; do not club them into one sentence.
  • Convert percentages to fractions/decimals in the first step; this makes your method transparent.
  • Box or underline final answers; it helps the examiner and reduces chance of marking errors.
  • Practice at least 10–12 word problems from NCERT and previous years' papers to build speed and accuracy.

Frequently asked questions

How do I know when to use a proportion versus a percentage in CBSE Class 7 Mathematics Chapter 10 problems?+
Use a proportion when the problem gives you two related quantities and asks you to find a third or fourth unknown in the same relationship (e.g., cost of 5 items vs. cost of 12 items). Use a percentage when the problem asks for a part of a whole on a 0-100 scale (e.g., discount, profit %, interest rate) or when comparing across different totals.
Why do we always divide profit by Cost Price and not Selling Price when calculating profit percentage?+
Profit % and Loss % measure the return or loss relative to the investment (Cost Price). Using SP would give a different base and make comparisons meaningless. For instance, a ₹10 profit on ₹50 CP is 20% profit, but on ₹60 SP it would appear as 16.67% — the first figure correctly shows the return on your investment.
My child's school uses a different textbook for Class 7 Mathematics. Will these notes still help for CBSE exams?+
Yes. All CBSE-affiliated schools must follow the official NCERT syllabus for Class 7 Mathematics, even if they use supplementary books. These notes are based on the 2024-25 NCERT curriculum for CBSE Class 7 Mathematics Chapter 10, so the concepts, formulas, and problem types will match your board exam. Your school book may have extra practice problems, but the core content is identical.
What is the difference between Simple Interest and Compound Interest, and which one is in CBSE Class 7 syllabus?+
Simple Interest (SI) calculates interest only on the principal for the entire period, using SI = (P × R × T) ÷ 100. Compound Interest (CI) calculates interest on the principal plus previously earned interest, compounding each period. CBSE Class 7 Mathematics Chapter 10 covers only Simple Interest; Compound Interest is introduced in Class 8 Comparing Quantities.
How do I simplify a ratio if the two numbers are large and I cannot easily find the HCF?+
Use the Euclidean algorithm (repeated division method) to find HCF. For example, to simplify 144:108, divide 144 by 108 → remainder 36; then divide 108 by 36 → remainder 0. So HCF = 36. Divide both terms: 144 ÷ 36: 108 ÷ 36 = 4:3. Alternatively, factor both numbers into primes and pick common factors, but the division method is faster for exams.
If a problem says '6 months at 8% per annum', do I use T = 6 or T = 0.5 in the SI formula?+
You must use T = 0.5 years, because the rate R is per annum (per year). Convert months to years by dividing by 12: T = 6 ÷ 12 = 0.5. Then SI = (P × 8 × 0.5) ÷ 100. If you mistakenly use T = 6, your interest will be twelve times too large, a common error in CBSE Class 7 Mathematics Chapter 10 exercises.
Can a ratio ever be greater than 1 or less than 1, and what does that mean?+
When expressed as a fraction, yes. The ratio 5:2 as a fraction is 5/2 = 2.5, which is greater than 1, meaning the first quantity is 2.5 times the second. The ratio 2:5 as a fraction is 2/5 = 0.4, meaning the first quantity is 0.4 times (or 40% of) the second. In simplest colon form, a ratio is just two whole numbers, but the fraction interpretation shows relative size.
What should I do if the NCERT exercise question asks to find CP when SP and profit % are given?+
Use the relationship SP = CP + Profit and Profit = (Profit % ÷ 100) × CP. Combine them: SP = CP + (Profit % ÷ 100) × CP = CP × (1 + Profit %/100). Rearrange to CP = SP ÷ (1 + Profit %/100). For example, if SP = ₹600 and profit % = 20%, then CP = 600 ÷ (1 + 20/100) = 600 ÷ 1.2 = ₹500. This reverse formula is tested in higher-level NCERT problems.
Are discounts calculated on Cost Price or Marked Price in CBSE Class 7?+
In CBSE Class 7 Mathematics Chapter 10, most problems use Cost Price and Selling Price. Marked Price (the price tag before discount) and discount calculations are introduced in Class 8 Comparing Quantities. If a Class 7 problem mentions discount, it usually means a percentage reduction applied to the given price, which you treat as the original price before discount.
How can I check if my answer to a proportion problem is correct?+
After solving, verify that the cross-products are equal. If your answer is a:b = c:d, compute a × d and b × c; they must be the same. For example, if you found x = 15 in the proportion 4:6 = 10:x, check: 4 × 15 = 60 and 6 × 10 = 60. Since 60 = 60, your answer is correct. This self-check takes seconds and catches arithmetic errors.
Why is understanding CBSE Class 7 Mathematics Chapter 10 Ratios, Proportions and Percentages important for competitive exams and Olympiads?+
Ratio, proportion, and percentage form the backbone of quantitative aptitude. Almost every competitive exam — NTSE, NMMS, school Olympiads, and later even CAT and bank exams — includes problems on these topics. Mastery at Class 7 gives you a strong foundation, saves time in later classes, and builds problem-solving confidence for tougher multi-step problems.
My child struggles with word problems in CBSE Class 7 Mathematics Chapter 10. What is the best way to improve?+
First, ensure strong conceptual clarity: can they state the formulas and explain why they work? Second, practice translating sentences into mathematical setups — write down what is given and what is asked before jumping into calculations. Third, solve 2–3 problems daily from NCERT exercises and RD Sharma. Fourth, use CBSETUTOR.ai to get instant step-by-step help on specific problems; the AI identifies exactly where the confusion lies and provides targeted explanations. Consistent daily practice for 15–20 minutes works better than marathon weekend sessions.

Keep learning — related guides

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