CSAT (Paper 2)
Reading Comprehension Logical Reasoning Quantitative Aptitude Decision Making
Module 2 · UPSC CSAT (Paper 2)

Quantitative Aptitude

Number system, percentages, profit-loss, time-work, speed-distance, data interpretation.
Number System · Percentages · Time-Work · Speed · DI
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Learning Objectives

  • Understand the fundamental concepts of Quantitative Aptitude
  • Apply key formulas and techniques to solve problems
  • Practice with exam-level questions to build speed and accuracy

Key Concepts

What is Quantitative Aptitude?

Quantitative Aptitude in UPSC CSAT tests basic numeracy and data interpretation skills at the class 10 level. Topics include number system, percentages, profit-loss, time-work, speed-distance, simple/compound interest, ratio-proportion, mensuration, and data interpretation. CSAT typically has 15-20 quant questions.

Key Concepts

1. Number System: Divisibility rules (2-11), LCM & HCF, remainder theorem, simplification using BODMAS, surds and indices, unit digit cyclicity. For CSAT, focus on speed of calculation rather than complex theory.

2. Percentages: Fraction-percentage equivalents (1/2=50%, 1/3≈33.33%, 1/4=25%, 1/5=20%, 1/6≈16.67%, 1/8=12.5%, 1/9≈11.11%). Successive change: net % = x + y + xy/100. Percentage change = (final-initial)/initial × 100.

3. Time & Work: Work = Rate × Time. If A does a job in n days, A's 1-day work = 1/n. Combined work: add individual rates. Efficiency inversely proportional to time.

4. Speed, Distance & Time: Speed = Distance/Time. 1 m/s = 18/5 km/h. Relative speed: towards each other = sum; same direction = difference. Average speed = total distance/total time.

5. Data Interpretation: Tables, bar graphs, line graphs, pie charts. Read the chart carefully, identify the quantities, and perform arithmetic. CSAT DI questions are straightforward but require careful reading to avoid misinterpretation.

Solved Examples

Example 1 (Percentage — Successive Change)
A number is increased by 20% and then decreased by 20%. What is the net percentage change?

a) 0% b) 4% increase c) 4% decrease d) 2% decrease
Solution: c) 4% decrease. Net = x + y + xy/100 = 20 + (-20) + (20×-20)/100 = 0 - 400/100 = -4%. Alternatively, if the initial number is 100: after 20% increase = 120, after 20% decrease = 120 - 24 = 96. Net change = -4%.
Example 2 (Time & Work)
A can complete a task in 12 days and B in 18 days. They work together for 4 days. How much work is left?

a) 1/3 b) 1/2 c) 4/9 d) 5/9
Solution: c) 4/9. A's 1-day work = 1/12, B's = 1/18. Combined = 1/12+1/18 = 5/36 per day. In 4 days, work done = 4×5/36 = 20/36 = 5/9. Work left = 1 - 5/9 = 4/9.
Example 3 (Speed — Average Speed)
A person travels from X to Y at 30 km/h and returns at 50 km/h. What is the average speed for the entire journey?

a) 37.5 km/h b) 40 km/h c) 42.5 km/h d) 45 km/h
Solution: a) 37.5 km/h. Average speed = 2ab/(a+b) where a=30, b=50. Average = 2×30×50/(30+50) = 3000/80 = 37.5 km/h.

Shortcut Techniques

  • Use fraction-percentage equivalents to speed up calculations — 12.5% = 1/8, 33.33% = 1/3, etc.
  • For successive change, remember the formula: x + y + xy/100 — works for two successive changes of any type (increase/decrease).
  • In time-work problems, take LCM of individual times as total work to avoid fractions.
  • In speed problems, ensure units are consistent — convert km/h to m/s (×5/18) or vice versa (×18/5).
  • For DI questions, estimate answers before calculating — often the answer choices are far apart, allowing estimation.
Pro Tip
CSAT quant is about speed and accuracy at a basic level. Master mental calculations — squares up to 30, cubes up to 20, fraction-decimal-percentage conversions. In the exam, the quant section can be time-consuming, so prioritise questions you can solve quickly and leave lengthy calculations for later.

Comprehensive Study Guide

Master quant aptitude with regular practice and concept clarity.

Practice Strategy

Phase 1: Learn concepts. Phase 2: Solve 30-40 basic questions. Phase 3: Attempt mixed-level questions. Phase 4: Take timed mocks. Phase 5: Analyze and improve.

Pro Tip
Consistency beats intensity. Study 1-2 hours daily rather than 6-8 hours on weekends.

Comprehensive Study Guide

Master quant aptitude with regular practice and concept clarity.

Practice Strategy

Phase 1: Learn concepts. Phase 2: Solve 30-40 basic questions. Phase 3: Attempt mixed-level questions. Phase 4: Take timed mocks. Phase 5: Analyze and improve.

Pro Tip
Consistency beats intensity. Study 1-2 hours daily rather than 6-8 hours on weekends.

Comprehensive Study Guide

Master quant aptitude with regular practice and concept clarity.

Practice Strategy

Phase 1: Learn concepts. Phase 2: Solve 30-40 basic questions. Phase 3: Attempt mixed-level questions. Phase 4: Take timed mocks. Phase 5: Analyze and improve.

Pro Tip
Consistency beats intensity. Study 1-2 hours daily rather than 6-8 hours on weekends.

Comprehensive Study Guide

Master quant aptitude with regular practice and concept clarity.

Practice Strategy

Phase 1: Learn concepts. Phase 2: Solve 30-40 basic questions. Phase 3: Attempt mixed-level questions. Phase 4: Take timed mocks. Phase 5: Analyze and improve.

Pro Tip
Consistency beats intensity. Study 1-2 hours daily rather than 6-8 hours on weekends.

Practice Questions

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