CTET · Study & Practice

Ratio, Proportion & Commercial Maths (VI–VIII)

AreaMathematics & Pedagogy DifficultyEasy–Moderate CTET weightage2–4 questions in the Mathematics section of Paper II (the commercial-arithmetic cluster is one of the most reliably tested topics)

Ratio, percentage, profit-and-loss and interest are the bread-and-butter of the upper-primary maths syllabus, and CTET Paper II treats them in two ways at once. About half the questions are straight computation — simplify a ratio, find a percentage, work out a selling price — pitched at exactly the level a Class VI–VIII teacher must be fluent in. The other half are pedagogy questions: a child writes 1/4 = 25 and you have to name the misconception, or you must pick the best way to introduce 'percent' to a Class VII class. This chapter keeps both halves in view. The numbers here are deliberately kept clean so you can check every step in your head, and each topic flags the standard errors children make — because those errors are themselves exam material.

Topics

1 Ratio, Proportion & Unitary Method 4 worked · 4 practice · 8-Q MCQ test Start → 2 Percentage 4 worked · 4 practice · 8-Q MCQ test Start → 3 Profit, Loss & Discount 4 worked · 4 practice · 8-Q MCQ test Start → 4 Simple Interest 4 worked · 4 practice · 8-Q MCQ test Start → 5 Direct & Inverse Proportion 4 worked · 4 practice · 8-Q MCQ test Start →

⚡ Smart tips & memory hooks

Memory hooks and exam-smart tips to lock this chapter in and answer CTET MCQs quickly and accurately.

  • Same unit FIRST, simplify SECOND: never compare or simplify a ratio until both quantities are in the same unit (minutes with minutes, ₹ with ₹).
  • Proportion check in one line: cross-multiply — extremes × extremes should equal means × means (a×d = b×c).
  • Percentage of a number: drop the two zeros — x% of 100 is just x, so 15% of 200 = 15 × 2 = 30.
  • Profit% and Loss% ALWAYS sit on CP; Discount% ALWAYS sits on MP. Get the base right and the arithmetic is trivial.
  • Simple Interest: write time in YEARS before plugging in (6 months = ½, 9 months = ¾). SI = PRT/100, then Amount = P + SI.
  • Direct vs inverse in two seconds: "if one goes up and the other goes up → direct (ratio fixed); if one up and the other down → inverse (product fixed)."

⚠️ Common mistakes & traps

CTET loves to test these exact confusions. Internalise each trap before exam day.

  • Comparing quantities in different units (e.g. 30 minutes to 1 hour written as 30 : 1 instead of 1 : 2).
  • Calculating profit% or loss% on the selling price instead of the cost price — the single most common commercial-maths error.
  • Confusing the marked price with the selling price and forgetting to subtract the discount.
  • Leaving the time in months in a simple-interest problem instead of converting to years (and confusing the Amount with the Interest).
  • Treating every variation problem as direct — multiplying in a "more workers, fewer days" question that is actually inverse.
  • Dropping the "per hundred" idea in percentage (writing 1/4 = 25 without the % sign, or thinking a percentage can never exceed 100).

📈 CTET exam insight & PYQ analysis

In CTET Paper II Mathematics this commercial-arithmetic cluster reliably yields 2–4 questions, split between pure computation and pedagogy. The computation favourites are: dividing a quantity in a given ratio, finding a percentage or a percent-of-marks, a profit/loss-percent calculation, a one-step simple-interest sum, and an inverse-proportion 'men and days' problem. The pedagogy items recur just as often — naming a child's misconception (profit% on SP, the 1/4 = 25 error, 'more is always more' in variation), choosing the best concrete introduction to percentage (the 100-grid) or to ratio (everyday 'for every' sharing), and identifying why an error is conceptual rather than careless. Expect the numbers to stay clean; CTET tests whether you understand the structure, not heavy calculation.

🎴 Flashcards — instant recall

Tap a card to reveal the answer. Drill these until they are automatic.

How do you put a ratio in simplest form?Tap to reveal
Make both terms the same unit, then divide both by their HCF.
What is the defining test of a proportion a : b :: c : d?Tap to reveal
Product of extremes = product of means, i.e. a × d = b × c.
What does "percent" literally mean?Tap to reveal
Per hundred — x% = x/100.
On which price are profit% and loss% always calculated?Tap to reveal
The Cost Price (CP). Profit% = (Profit/CP) × 100.
On which price is discount% always calculated?Tap to reveal
The Marked Price (MP). SP = MP − Discount.
State the simple interest formula and the amount.Tap to reveal
SI = (P × R × T)/100; Amount = P + SI.
In simple interest, what unit must the time T be in?Tap to reveal
Years — convert months to years (6 months = ½ year).
What stays constant in direct proportion? In inverse?Tap to reveal
Direct: the ratio x/y. Inverse: the product x × y.
Workers and days for a fixed job are in which proportion?Tap to reveal
Inverse — more workers, fewer days (product constant).
A child writes profit% = profit/SP × 100. What is wrong?Tap to reveal
The base is wrong — profit% is taken on CP, not SP.
Best concrete way to introduce 'percent' in Class VII?Tap to reveal
The 100-grid (10 × 10 square) — shade "so many out of a hundred".
A child says 1/4 = 25. What misconception is this?Tap to reveal
Dropping the "per hundred" idea — it is 25%, i.e. 25/100, not 25.

📌 Quick revision

This commercial-arithmetic chapter covers five linked ideas. RATIO compares same-unit quantities by division and is simplified via the HCF; PROPORTION equates two ratios and is tested by cross-multiplication (extremes × means); the unitary method ('find one unit first') underlies both. PERCENTAGE is just 'per hundred' — x% = x/100 — and is best introduced with the 100-grid. In PROFIT & LOSS, profit/loss percent are always on the cost price while discount is always on the marked price. SIMPLE INTEREST is SI = PRT/100 with time in years and Amount = P + SI. DIRECT proportion keeps the ratio constant (more, more); INVERSE keeps the product constant (more, less). For each, know the children's misconceptions — wrong base, dropped % sign, unconverted months, 'more is always more' — because CTET tests the pedagogy as hard as the sum.

Chapter test

📝 Ratio, Proportion & Commercial Maths (VI–VIII) — Chapter Test
25 fresh questions · timed · full solutions
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📚 Want the full concept lesson?

This chapter gives you the CTET-focused recap, pedagogy and exam-style practice. For the underlying concept taught step by step — worked from the ground up with diagrams — open the matching lesson in our school Maths course.

🔗 See the full lesson in our Class 6–8 Maths course
Optional deep-dive · full Class 6–8 teaching · diagrams & worked steps
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🏆 Vidaara CTET success checklist

You have truly mastered Ratio, Proportion & Commercial Maths (VI–VIII) when you can tick every box below.

  • Recall every formula in this chapter without looking them up
  • Solve each topic’s practice set with at least 80% accuracy
  • Use the chapter shortcuts to cut your solving time in half
  • Spot and avoid every common trap listed above
  • Score 80%+ on the timed chapter test

📋 Chapter mastery scorecard

Track where you stand. Aim for the target before moving to the next chapter.

Skill checkpointTarget
Concept theory & formulas understood100%
Topic practice sets attempted (5 topics)5/5
Best topic-test score— → 80%+
Chapter test score— → 80%+
Flashcards drilled to instant recall12 cards