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Syllabus
⚖️ CLAT
Subject:Common Law Admission Test Syllabus

Basic Mathematics & Data Interpretation

Syllabus Unit: Quantitative Techniques

Why it matters

Chapter overview

CLAT's Quantitative Techniques section tests Class 10-level mathematics applied to short passages and data sets rather than isolated numerical problems — you're expected to extract the relevant figures from a table, graph, or paragraph and then apply percentages, ratios, averages, profit-loss, interest, speed, or mensuration formulas quickly and accurately. This unit covers the four pillars: percentages/ratio/averages, profit-loss/interest/speed, data interpretation from tables and graphs, and basic geometry/mensuration.

Common Law Admission Test Syllabus Quantitative Techniques 10% weightage
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Core Quant Tools
1PercentageChange ÷ original × 100
2Ratioa:b relative comparison
3AverageSum ÷ count

1Percentages, Ratio & Averages

Percentages, ratios, and averages are the three most-used tools in CLAT's quantitative section — nearly every other calculation builds on them.

Learning Objectives

  • Convert fluently between fractions, decimals, and percentages, and compute percentage increase/decrease correctly using the original base value.
  • Apply ratio and proportion to split a quantity, and solve for an unknown in a proportion using cross-multiplication.
  • Compute simple, weighted, and combined averages, and know how average shifts when a data point is added or removed.
  • Recognise the classic percentage-change trap of dividing by the wrong (new instead of original) base value.

Key Terms

Percentage Change(New Value − Original Value) ÷ Original Value × 100 — always computed relative to the ORIGINAL value, not the new one.
RatioA comparison of two quantities of the same kind, expressed as a:b, indicating their relative sizes without stating absolute values.
ProportionA statement that two ratios are equal (a:b = c:d), solvable by cross-multiplication: a×d = b×c.
Weighted AverageAn average where each value is multiplied by its own weight/frequency before summing and dividing by total weight, rather than treating all values equally.

**Percentages, ratios, and averages** are the computational backbone of CLAT's quantitative section — nearly every profit-loss, interest, speed, or DI question ultimately reduces to one of these three operations.

Percentages

Percentage Change = [(New − Original) ÷ Original] × 100
Common MistakeAlways divide by the ORIGINAL (starting) value, never the new value — this single error is the most common percentage mistake in CLAT quant.

Ratio and proportion

A ratio a:b compares two quantities directly. To split a total T in the ratio a:b, the two parts are T×a/(a+b) and T×b/(a+b). A proportion states two ratios are equal (a:b = c:d) and is solved by cross-multiplication: a×d = b×c.

Averages

  • Simple average = Sum of values ÷ Number of values.
  • Weighted average = Σ(value × weight) ÷ Σ(weights) — used when values don't carry equal importance (e.g., average marks across subjects with different credit hours).
  • When a new value replaces an old one in a group, the change in average = (new value − old value) ÷ total number of items.
New Average = (Old Sum + New Value) ÷ (Old Count + 1)