SSC CGL Quant · Study & Practice

Average, Mixture & Alligation

AreaArithmetic DifficultyEasy–Moderate SSC weightage3–5 questions

Average is total divided by count — but SSC rarely asks it that plainly. It dresses it up as a changed average when a person joins or leaves, an innings score, or an average speed for a two-leg journey. Alligation is the partner idea: a fast visual rule for the ratio in which two ingredients (or two prices, or two speeds) must mix to hit a target average. Learn the cross rule and weighted-average problems become ten-second cross-multiplications.

Topics

1 Average Basics 4 worked · 5 practice · 8-Q test Start → 2 Weighted Average 4 worked · 5 practice · 8-Q test Start → 3 Alligation Rule 4 worked · 5 practice · 8-Q test Start → 4 Mixtures & Replacement 4 worked · 5 practice · 8-Q test Start →

⚡ SSC shortcuts & speed methods

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

  • Think in totals when a value is added/removed: change in total = n x change in average.
  • Average speed for equal distances = 2ab/(a+b) (harmonic mean), NOT (a+b)/2.
  • Alligation cross: cheaper:dearer = (dearer - mean):(mean - cheaper).
  • Repeated replacement: remaining = initial x (1 - r/V)^n.

⚠️ Common mistakes & traps

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

  • Averaging two averages without weighting by group size.
  • Using (a+b)/2 for average speed when distances (not times) are equal.
  • Flipping the alligation diagonals (cheaper goes with the dearer-difference).
  • Forgetting the replacement decay is multiplicative, not subtractive.

📈 SSC exam insight & PYQ analysis

SSC mixes changed-average (innings, replacement), weighted average (two sections/mix prices) and alligation for alloy/milk problems. Liquid replace-and-top-up is a recurring Tier-2 item.

🎴 Flashcards — instant recall

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

Average speed, equal distances a, b?Tap to reveal
2ab/(a+b)
Alligation ratio rule?Tap to reveal
cheaper:dearer = (dearer-mean):(mean-cheaper)
Milk left after n replacements?Tap to reveal
V x (1 - r/V)^n
Sum from average?Tap to reveal
average x count
40@60 and 60@70 combined avg?Tap to reveal
66

📌 Quick revision

Work averages through totals; weight by group size; use the alligation cross to find mix ratios; and apply (1 - r/V)^n for repeated liquid replacement. Average-speed for equal distances is the harmonic mean 2ab/(a+b).

Chapter test

📝 Average, Mixture & Alligation — Chapter Test
25 fresh questions · timed · full solutions
Start chapter test →
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🏆 Vidaara SSC success checklist

You have truly mastered Average, Mixture & Alligation 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 (4 topics)4/4
Best topic-test score— → 80%+
Chapter test score— → 80%+
Flashcards drilled to instant recall5 cards