Maths Capsules for Competitive Exams – Complete Arithmetic Guide

Maths Capsules for Competitive Exams: The Ultimate Guide to Master Arithmetic for PSC, SSC, UPSC, RRB & All Govt Exams

Meta Title: Maths Capsules for Competitive Exams – Complete Arithmetic Guide
Meta Description: Learn important maths capsules for PSC, UPSC, SSC, RRB & banking exams. Covers arithmetic shortcuts, formulas, examples, tricks, and practice tips for fast calculation.

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Mathematics is one of the most scoring subjects in any competitive exam. Whether you are preparing for PSC, UPSC CSAT, SSC CGL/CHSL, RRB NTPC/Group D, Bank PO/Clerk, or state exams — Arithmetic contributes nearly 60–70% of the quantitative aptitude section.

To help candidates revise quicker and score higher, here is a complete and comprehensive Maths Capsule covering all key arithmetic topics, formulas, shortcuts, examples, and exam-oriented tips.

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What Are Maths Capsules?

Maths capsules are short, powerful revision notes containing:

• Key formulas

• Shortcuts/tricks

• Concept summaries

• Examples

• Fast solving approaches

They help candidates revise the entire arithmetic syllabus in less time, especially during last-minute preparation.

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Syllabus Covered in Arithmetic Maths Capsule

✔ Number System
✔ HCF & LCM
✔ Simplification & Approximation
✔ Percentage
✔ Profit & Loss
✔ Discount
✔ Simple Interest
✔ Compound Interest
✔ Ratio & Proportion
✔ Partnership
✔ Time & Work
✔ Pipes & Cistern
✔ Time, Speed & Distance
✔ Boat & Stream
✔ Train Problems
✔ Mixture & Alligation
✔ Average
✔ Age Problems
✔ Algebra Basics
✔ Mensuration (2D & 3D)
✔ Probability & Permutation – Basic level

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CHAPTER-WISE DETAILED MATHS CAPSULE

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1️⃣ Number System Capsule

Important Concepts

• Natural, Whole, Integers, Rational, Irrational

• Divisibility rules for 2,3,4,5,6,8,9,10,11

• Remainder theorem

• Cyclicity of numbers (units digit patterns)

Key Formulas

• Even × Even = Even

• Odd × Odd = Odd

• Even × Odd = Even

Tricks

• For last digit of a power: check cycle

  • Example: 2ⁿ → 2,4,8,6 (cycle of 4)

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2️⃣ HCF & LCM Capsule

HCF Formula

• For two numbers:
  HCF × LCM = Product of numbers

LCM of fractions:
LCM = LCM (Numerators) / HCF (Denominators)

HCF of fractions:
HCF = HCF (Numerators) / LCM (Denominators)

Exam Tip:
Always prime factorize large numbers.

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3️⃣ Simplification & Approximation

Rules

• BODMAS

• Convert fractions to approx values

• Square values up to 30

• Cube values up to 20

Shortcut

• 1/3 = 0.333

• 1/6 = 0.166

• 1/8 = 0.125

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4️⃣ Percentage Capsule

Basic formula:
Percentage = (Value / Total) × 100

Increase/Decrease Trick

• A%↑ followed by B%↓ → Net % = A – B – (AB/100)

Important Values

• 50% = 1/2

• 25% = 1/4

• 12.5% = 1/8

• 6.25% = 1/16

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5️⃣ Profit, Loss & Discount

Formulas

• Profit = SP – CP

• Loss = CP – SP

• Profit % = (Profit / CP) × 100

• Discount = MP – SP

• Discount % = (D / MP) × 100

Successive Discount:
D = A + B – (AB/100)

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6️⃣ Simple Interest (SI) & Compound Interest (CI)

SI Formula
SI = (P × R × T) / 100

CI Formula
CI = P(1 + R/100)ᵀ – P

Difference between CI & SI (2 years)
CI – SI = P (R² / 10000)

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7️⃣ Ratio & Proportion

Formulas

• Ratio a:b = a/b

• If a:b = c:d → proportion

Important Concept

• If ratio increases → add

• If ratio decreases → subtract

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8️⃣ Partnership

Rule:
Money × Time = Share

If partner joins late:
Use time difference in months.

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9️⃣ Time & Work Capsule

Core Formula:
Work = Rate × Time

If A does work in X days → one day work = 1/X

LCM method
Assign total work = LCM of time values.

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🔟 Pipes & Cistern

• Inlet → fills work

• Outlet → empties work

Net work per hour = Inlet – Outlet

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1️⃣1️⃣ Time, Speed & Distance (TSD)

Speed = Distance / Time
Time = Distance / Speed
Distance = Speed × Time

Conversions
1 km/hr = 5/18 m/s
1 m/s = 18/5 km/hr

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1️⃣2️⃣ Boat & Stream

Formulas
Downstream = u + v
Upstream = u – v

Speed of boat = (D + U) / 2
Speed of stream = (D – U) / 2

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1️⃣3️⃣ Trains Problems

Relative speed concept

• Same direction → subtract speeds

• Opposite direction → add speeds

Time = Distance / Relative Speed

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1️⃣4️⃣ Mixture & Alligation Capsule

Important Formula
New Concentration =
(Remaining × Old% + Added × New%) / Total Qty

Alligation Rule:
(High – Mean) : (Mean – Low)

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1️⃣5️⃣ Averages

Average = Sum / Number of items

If one value replaced:
New Avg = Old Avg + (Difference / N)

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1️⃣6️⃣ Age Problems

Present age → x
Future age → x + n
Past age → x – n

Use ratio method for faster solving.

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1️⃣7️⃣ Mensuration Capsule

2D Formulas

• Square → a²

• Rectangle → l × b

• Triangle → ½bh

• Circle → πr²

3D Formulas

• Cube → a³

• Cuboid → l × b × h

• Cylinder → πr²h

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1️⃣8️⃣ Probability (Basic)

Probability = Favourable / Total outcomes

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1️⃣9️⃣ Permutation & Combination (Basic)

Permutation (arrangement):
nPr = n! / (n – r)!

Combination (selection):
nCr = n! / r!(n – r)!

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How to Score 40+/50 in Quant (SSC, RRB, Bank)

✔ Master tables, squares, cubes

✔ Learn all formulas

✔ Practice at least 30–40 questions daily

✔ Solve mock tests

✔ Revise capsules daily

✔ Improve accuracy + speed

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Final Words

Maths capsules help you revise the entire arithmetic syllabus quickly, making them perfect for:

• PSC

• SSC (CGL, CHSL, GD)

• UPSC CSAT

• RRB NTPC / Group D

• Banking exams (IBPS/SBI)

• Defence exams

• State competitive tests

Consistent practice + smart revision = High marks in Quantitative Aptitude.