Module 1 · Arithmetic
Chapter 3: Ratio & Proportion
Arithmetic
5 topics
🎯 1 practice questions
What this chapter covers
The 5 topics below make up Ratio & Proportion on the CAT. Click any topic to open its notes, examples and practice test.
1Basic & Compound Ratio
2Continued Ratio
3Proportion
4Direct & Inverse Variation
5Mean & Third Proportion
Study material & tests
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Notes, worked examples and hint-guided practice for every topic.
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🎯 Topic tests
8 auto-graded questions per topic, pulled from the question bank.
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📝 Chapter test
25 fresh mixed-difficulty questions, timed, with full solutions.
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Formula Reference Sheet
This chapter
Ratio essentials
| Ratio of a to b | a : b = a/b (b ≠ 0) |
|---|---|
| Scaling a ratio | a : b = ka : kb for any k ≠ 0 |
| Compound ratio | (a:b) × (c:d) = ac : bd |
| Duplicate / triplicate | a²:b² (duplicate), a³:b³ (triplicate) |
| Dividing N in a:b | shares = aN/(a+b) and bN/(a+b) |
Proportion & variation
| Proportion | a:b = c:d ⇒ a×d = b×c (product of extremes = product of means) |
|---|---|
| Mean proportional of a, b | √(ab) |
| Third proportional to a, b | b²/a |
| Fourth proportional to a, b, c | bc/a |
| Direct variation | y = kx (y/x constant) |
| Inverse variation | y = k/x (xy constant) |
CAT reference
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