Mathematics & Its Pedagogy
Ratio, Proportion & Commercial Maths (VI–VIII)
Mathematics & Pedagogy
Paper II
5 topics
What this chapter covers
The 5 topics below make up Ratio, Proportion & Commercial Maths (VI–VIII) in the CTET syllabus. Open any topic for notes, solved examples and a practice MCQ test.
1Ratio, Proportion & Unitary Method
2Percentage
3Profit, Loss & Discount
4Simple Interest
5Direct & Inverse Proportion
Study material & tests
📚 Study this chapter
Concept notes, key points, solved examples and hint-guided practice for every topic.
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🎯 Topic MCQ tests
8 auto-graded CTET-style questions per topic, with full explanations.
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📝 Chapter test
25 fresh mixed-difficulty questions, timed, with solutions.
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Key Concepts — Quick Reference
This chapter
Ratio, proportion & percentage
| Ratio in simplest form | a : b = (a ÷ HCF) : (b ÷ HCF) |
|---|---|
| Proportion | a : b :: c : d ⇔ a × d = b × c (product of extremes = product of means) |
| Unitary method | value of 1 unit = total ÷ number of units |
| Percentage | x% of N = (x / 100) × N ; what % is a of b = (a / b) × 100 |
Commercial maths
| Profit / Loss | Profit = SP − CP ; Loss = CP − SP (when SP < CP) |
|---|---|
| Profit % / Loss % | Profit% = (Profit / CP) × 100 ; Loss% = (Loss / CP) × 100 (always on CP) |
| Discount | Discount = MP − SP ; Discount% = (Discount / MP) × 100 (always on MP) |
| Simple Interest | SI = (P × R × T) / 100 ; Amount = P + SI |
| Direct / Inverse variation | Direct: x / y = k (constant); Inverse: x × y = k (constant) |