Chapter Overview

Basic Numeracy is the arithmetic core of CGPSC Prelims Paper II (CSAT): the Class X-level number skills that every word problem, data table and reasoning puzzle quietly depends on. Nothing here needs higher mathematics. What it needs is a handful of shortcuts practised until they are automatic, because Paper II gives you 100 questions in 2 hours.

What You’ll Learn

By the end of this chapter, you’ll be able to:

Switch between fractions, decimals and percentages instantly
Handle percentage change, successive changes, percentage points and population/price growth
Combine and divide ratios, find proportionals, and solve mixture, coin, partnership and age problems
Work with averages — weighted averages, replacement and wrong-entry questions, and average speed
Solve each standard question type in under a minute

Prerequisites

Before starting this chapter, you should be comfortable with:

Multiplication tables up to 20 and squares up to 25
Fractions, decimals, HCF and LCM (Class VI–VIII level)
Forming and solving a simple linear equation in one unknown

Learning Path

Follow these topics in order — each builds on the one before:

graph TD
    A[Fractions and decimals] --> B[1. Percentages]
    B --> C[2. Ratio and Proportion]
    C --> D[3. Averages]
    D --> E[Quick Revision sheet]
    E --> F[Data Interpretation]
    B -.-> F

Topics in This Chapter

Topic	Description	Time
Percentages	Fraction–percent table, percentage change, successive change, percentage points, population and price growth	12 min
Ratio and Proportion	Combining ratios, dividing amounts, proportionals, mixtures, coins, partnership and ages	12 min
Averages	Sum–count method, number patterns, weighted averages, replacement, wrong entries, average speed	10 min
Quick Revision	Every formula and shortcut from the chapter on one page	5 min

Coming next in this chapter

Number system, profit and loss, and time and work are also part of the numeracy syllabus and will be added here. Percentages and ratios are the foundation for all three.

Where It Is Asked

Paper	How numeracy appears
Prelims Paper II (CSAT)	Objective MCQs on percentages, ratios, averages and related arithmetic, at Class X level. 100 questions, 200 marks, 2 hours.
Mains Paper IV (GS-II)	The reasoning-and-mathematics part (Part 2) tests the same arithmetic, where the working counts as well as the answer.

Paper II is qualifying — but you must qualify

Prelims Paper II marks are not added to your merit, but you must cross the minimum qualifying mark — commonly cited as 33%, though the exact threshold can vary by category, so check the current CGPSC notification. Wrong answers carry negative marking of one-third of the question’s marks, so a careless guess costs you. Numeracy is the most dependable block for crossing the line: the methods are fixed and the answers are exact.

Numeracy also runs through the other CSAT chapters: Data Interpretation is percentages, ratios and averages applied to tables and charts; General Mental Ability and Logical Reasoning reward the same number sense.

Quick Reference

Key Formulas

Concept	Formula
Percentage change	\( \frac{\text{New} - \text{Old}}{\text{Old}}\times 100 \)
Successive change	\( a + b + \frac{ab}{100} \)
A is r% more than B	B is \( \frac{r}{100+r}\times 100\% \) less than A
Compound growth	\( P\left(1 + \frac{r}{100}\right)^n \)
Proportion	\( a : b :: c : d \iff ad = bc \)
Mean proportional	\( \sqrt{ab} \)
Partnership	Profit \( \propto \) capital \( \times \) time
Weighted average	\( \frac{n_1 a_1 + n_2 a_2}{n_1 + n_2} \)
Average speed (equal distances)	\( \frac{2xy}{x+y} \)

Exam Focus

High-yield: successive percentage change, “more than / less than” asymmetry, combining ratios, weighted averages, average speed.
Favourite traps: adding successive percentages, percent vs percentage point, averaging averages of unequal groups, ignoring time in partnership.
Speed target: each standard question in under 60 seconds — every topic page ends with a timed speed drill.

Start Learning

Ready to begin? Start with the first topic:

→ Percentages