Quantitative Aptitude (QA) is a crucial section in the SSC CGL exam, often making the difference between a good and a great score. If numbers intimidate you or calculations slow you down, don’t worry! With the right approach, mastering formulas and improving speed is entirely possible. In this guide, we’ll break down essential formulas, calculation tricks, and strategies to help you ace the QA section effortlessly.
Why Mastering Formulas and Calculations is Important?
SSC CGL QA tests your ability to solve numerical problems quickly and accurately. A strong grasp of formulas helps you:
- Save time during calculations.
- Improve accuracy and minimize errors.
- Solve complex questions efficiently.
- Boost confidence during the exam.
Let’s dive into the key formulas and tricks you need to succeed!
Essential Formulas for SSC CGL QA
1. Percentage & Profit-Loss
- Percentage change = Percentage Change= (new value−original value)original value×100
- Profit % = Profit percentage = (Profit/Cost Price) × 100
- Loss % = Loss % = Loss/Cost Price × 100
2. Average & Ratio-Proportion
- Average = Sum of Observations/ Number of Observations
- If A : B = x : y and B : C = p : q, then A : B : C = x : y : q
4. Time, Speed & Distance
- Speed = Distance / Time
- Time = Distance / Speed
- If two objects move towards each other, their relative speed = (Speed 1 + Speed 2)
- If two objects move in the same direction, relative speed = |Speed 1 – Speed 2|
5. Algebra & Geometry
- (a + b)2 = a2 + 2ab + b2 = (a – b)2 + 4ab
- (a – b)2 = a2 – 2ab + b2 = (a + b)2 – 4ab
- (a2 + b2) = (a + b)2 – 2ab = (a – b)2 + 2ab
- (a2 – b2) = (a – b)(a + b)
- 2(a2 + b2) = (a + b)2 + (a – b)2
- (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
- (a + b – c)2 = a2 + b2 + c2 + 2ab – 2bc – 2ca
- (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
- (a + b)3 = a3 + b3 + 3ab(a + b)
- (a – b)3 = a3 – b3 – 3ab(a – b)
- (a3 – b3) = (a – b) (a2 + ab + b2) = (a – b)3 + 3ab(a – b)
- (a3 + b3) = (a + b) (a2 – ab + b2) = (a + b)3 – 3ab(a + b)
- 2(a2 + b2) = (a + b)2 + (a – b)2
- a3 + b3 + c3 – 3abc = 1/2 (a + b + c) {(a – b)2 + (b – c)2 + (c – a)2}
- If a + b + c = 0, then a3 + b3 + c3 = 3abc
- am × an = a(m + n)
- am/an = a(m – n)
- (am)n = am × n
6. Mensuration 2D
| Name | Perimeter | Area |
| Rectangle | 2 (a + b) | ab |
| Square | 4a | a2 |
| Triangle | a + b + c = 2s | 1. ½ × b × h 2. √(s(s – a)(s – b)(s – c) |
| Sector of a circle | l + 2r where l = (θ/360) × 2πr | θ/360° × πr2 |
| Semicircle | πr + 2r | ½ πr2 |
| Circle | 2πr | πr2 |
| Trapezium | Sum of its four sides | ½ × h × (a + b) |
| Rhombus | 4a | ½ d1d2 |
| Parallelogram | 2(a + b) | ah |
| Isosceles right triangle | 2a + d | ½ a2 |
| Equilateral triangle | 3a | 1 . ½ ah 2. √3/4 a2 |
| Right triangle | b + h + d | ½ bh |
7. Mensuration 3D
| Solid | Lateral/Curved Surface Area | Total Surface Area | Volume |
| Cuboid | 2(l + b)h | 2(lb + bh + hl) | lbh |
| Cube | 4l2 | 6l2 | l3 |
| Right circular cone | 2πrh | 2πr(r + h) | πr2h |
| Sphere | 4πr2 | 4πr2 | 3πr3 |
| Hemisphere | 2πr2 | 3πr2 | 2/3πr3 |
| Frustum of right circular cone | π(R + r)l where R & r are radii of base and R>r and l = √(h2 + (R – r)2 | πl(R + r) + πr2 + πR2 | 1/3πh(R2 + r2 + Rr) |
| Hollow cylinder | 2π(R + r)h Where R = external radius and r = internal radius | 2π(R + r)h + 2π(R2 – r2)h | π(R2 – r2) |
Calculation Tricks to Improve Speed
- Use Approximation Techniques
- Round off numbers to make calculations easier.
- Example: Instead of multiplying 198 × 12, approximate it to 200 × 12 = 2400 and adjust accordingly.
- Master the Multiplication Shortcuts
- Multiply numbers close to 100 using the Base Method:
- Example:
- Base = 100
- (103 – 100) × (107 – 100) = 3 × 7 = 21
- Add the base: 103 + 7 = 110
- Answer: 11021
- Multiply numbers close to 100 using the Base Method:
- Use the Unit Digit Trick
- Quickly eliminate options in MCQs by checking the unit digit of calculations.
- Apply Square & Cube Shortcuts
- Squares of numbers ending in 5:
- Example: attach 25 → 625
- Practice Vedic Math Techniques
- Cross Multiplication for quick division.
- The “Criss-Cross” method for two-digit multiplications.
- Percentage Calculations
Move the decimal one place left to find 10%. Example: 10% of 350 is 35. - Simplification Techniques
Break down complex expressions using distributive property and common factors. - Multiplication Shortcuts
Break numbers into simpler components. Example: (30 + 5) × 25 = (30 × 25) + (5 × 25) - Division Tricks
Use divisibility rules (2, 3, 5, 9, 10) to quickly determine divisibility. - Quick Addition/Subtraction
Group numbers (hundreds, tens, units) to simplify calculations. - Square and Cube Roots
Approximate square roots by knowing squares of numbers close to the given value. - Time and Distance Problems
Solve using relative speed concepts for moving objects in different directions. - Profit and Loss
Calculate selling price for a 25% profit by multiplying cost price by 1.25. - Averages
Compute weighted averages by multiplying values by weights and dividing by total weight. - Data Interpretation
Analyze graphs to understand trends and answer related questions efficiently.
How to Apply This in SSC CGL Preparation?
- Daily Formula Revision: Spend 15 minutes revising key formulas.
- Timed Practice Sessions: Solve 10-15 questions daily under a timer.
- Mock Tests & Analysis: Attempt full-length tests to improve time management.
- Shortcut Implementation: Start with slow practice, then integrate shortcuts into problem-solving.
Avoid These Common Mistakes
- Memorizing Without Understanding: Ensure you understand concepts behind formulas.
- Skipping Basics: Don’t ignore foundational topics like Number Systems and BODMAS.
- Lack of Practice: The more you practice, the better your calculation speed.
- Ignoring Accuracy: Speed is important, but accuracy wins the game.
Final Thoughts
Mastering SSC CGL QA is all about practice, consistency, and strategy. Learn the essential formulas, apply calculation tricks, and regularly take mock tests to track your progress.
Want to supercharge your SSC CGL prep? Download the NetPractice app! Access topic-wise quizzes, mock tests, and detailed performance analysis to sharpen your skills and boost your confidence.
Stay focused, keep practicing, and you’ll ace the QA section in no time!
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