CAT Quant · Study & Practice

Ratio & Proportion

AreaArithmetic DifficultyEasy–Moderate CAT weightage2–4 questions (directly + inside Mixtures, Partnership, Time-Work, SI/CI, DI)

Ratio and proportion is the quiet workhorse of CAT Arithmetic. A ratio compares two quantities of the same kind by division, and proportion is simply the statement that two ratios are equal — yet almost every "applied" chapter leans on these two ideas. Partnership profits split in the ratio of capital × time, mixtures and alligation rest on weighted ratios, time-and-work shares are inverse ratios of efficiency, and even data interpretation tables are read as ratios in disguise. CAT rarely asks "simplify 12:18"; it hides ratios inside multi-quantity word problems and rewards the student who can scale a whole chain (a:b:c:d) with a single common multiplier, switch fluently between direct and inverse variation, and back-solve from a difference or a total. This chapter builds that fluency: combining and compounding ratios, stitching separate ratios into one continued ratio, the four members of a proportion, direct and inverse variation, and the mean and third proportionals — each with worked examples, the fastest exam method, and the traps that quietly cost marks.

Topics

1 Basic & Compound Ratio 4 worked · 5 practice · 8-Q test Start → 2 Continued Ratio 4 worked · 5 practice · 8-Q test Start → 3 Proportion 4 worked · 5 practice · 8-Q test Start → 4 Direct & Inverse Variation 4 worked · 5 practice · 8-Q test Start → 5 Mean & Third Proportion 4 worked · 5 practice · 8-Q test Start →

⚡ CAT shortcuts & speed methods

The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.

  • Write any ratio a:b as a common multiple ak:bk so a total or difference collapses to one equation in k.
  • To combine a:b and b:c, scale each so the shared term equals the LCM of its two values, then chain (a:b:c).
  • Compound ratios multiply part-wise: (a:b)×(c:d) = ac:bd. Areas use squares (a²:b²), volumes use cubes (a³:b³).
  • Compare two ratios by cross-multiplying: a:b > c:d exactly when ad > bc — no decimals needed.
  • In a proportion a:b = c:d, product of extremes = product of means (ad = bc); cross-multiply instantly.
  • Mean proportional of a, b = √(ab); third proportional = b²/a; fourth proportional = bc/a. Mark the repeated term.

⚠️ Common mistakes & traps

CAT is designed so that careless errors here cost you marks. Internalise each trap before the exam.

  • Comparing ratios in different units (paise vs rupees, grams vs kg) without converting first.
  • Adding the parts of a:b directly to a total instead of splitting the total as aN/(a+b) and bN/(a+b).
  • Forgetting to equalise the shared term before combining two ratios into a continued ratio.
  • Treating an inverse relationship (men–days, speed–time) as direct, so the answer moves the wrong way.
  • Mixing up the third proportional (b²/a) with the mean proportional (√ab) or the fourth proportional (bc/a).

📈 CAT exam insight & PYQ analysis

In recent CAT and XAT papers, pure ratio questions are uncommon as standalone items; ratios surface chiefly inside Mixtures and Alligation, Partnership, Time–Work, Time–Speed–Distance and Data Interpretation. The recurring patterns are: stitching two or three ratios into one continued ratio, splitting a total in a given ratio, the men–days–work inverse-variation family, and mean/third proportional one-liners. Difficulty is Easy–Moderate alone but climbs when combined with variation or DI, where clean common-multiplier work and avoiding the direct-versus-inverse trap decide your speed and accuracy.

🎴 Flashcards — instant recall

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

Compound ratio of (a:b) and (c:d)?Tap to reveal
ac : bd
Duplicate ratio of a:b?Tap to reveal
a² : b²
Triplicate ratio of a:b?Tap to reveal
a³ : b³
How to combine a:b and b:c?Tap to reveal
Equalise b via its LCM, then chain a:b:c
Proportion a:b = c:d implies?Tap to reveal
a×d = b×c (extremes = means)
Mean proportional of a and b?Tap to reveal
√(ab)
Third proportional to a and b?Tap to reveal
b²/a
Fourth proportional to a, b, c?Tap to reveal
bc/a
Direct variation relation?Tap to reveal
y = kx (y/x constant)
Inverse variation relation?Tap to reveal
y = k/x (xy constant)
Split N in the ratio a:b — first share?Tap to reveal
aN/(a+b)
Componendo–dividendo: a:b from (a+b):(a−b) = m:n?Tap to reveal
a:b = (m+n):(m−n)

📌 Quick revision

A ratio compares like quantities and scales freely (a:b = ka:kb). Combine ratios by equalising the shared term via its LCM, and split a total as aN/(a+b). Compound ratios multiply part-wise; areas square the ratio, volumes cube it. A proportion means a:b = c:d, so extremes × = means × (ad = bc). Mean proportional = √(ab), third proportional = b²/a, fourth proportional = bc/a. Direct variation keeps y/x constant; inverse variation keeps xy constant — more men, fewer days. Avoid the traps: convert units first, never treat inverse as direct, and mark the repeated term before applying a proportional formula.

Chapter test

📝 Ratio & Proportion — Chapter Test
25 fresh questions · timed · full solutions
Start chapter test →
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🏆 Vidaara CAT success checklist

You have truly mastered Ratio & Proportion 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