Aptitude
Aptitude is a key part of most placement and company screening rounds. It checks how fast you can think, calculate, and make logical decisions — often under time pressure.
This document collects everything needed to master aptitude — from core formulas to real-world business math, and links to detailed cheat sheets and practice resources that together cover nearly every type of question asked in tests.
Complete Reference PDFs
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🧾 102-Page Aptitude Tricks PDF — Download here
Covers almost every aptitude question type — with formulas, shortcuts, and solved examples.
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📘 Quantitative Aptitude Cheat Sheet (Bank Exams Today) — QT-Cheatsheet.pdf
Great for quick revisions — clear formula summaries and common question types.
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🎥 Full Aptitude Crash Course (YouTube) — Placement Preparation Series
Fast visual recap for quantitative and logical aptitude sections.
Core Topics
| Category | Subtopics |
|---|---|
| Quantitative Aptitude | Percentages, Profit & Loss, Growth & Revenue, Ratio & Proportion, Time & Work, Time–Speed–Distance, Simple & Compound Interest |
| Logical Reasoning | Puzzles, Series, Data Interpretation |
| Probability & Combinatorics | Probability, Permutations, Combinations |
| Business Aptitude | Growth %, Market Share, ROI, Equity & Ownership, Valuation basics |
Important Formulas (Quick Recall)
📈 Percentages & Growth
- % = (Value / Total) × 100
- Growth % = ((New – Old) / Old) × 100
- Successive % Change = a + b + (ab / 100)
- Revenue = Price × Quantity
- Profit Margin = (Profit / Revenue) × 100
💰 Profit, Loss & Discount
- Profit = SP – CP, Loss = CP – SP
- Profit % = (Profit / CP) × 100
- Selling Price = CP × (1 + Profit% / 100)
- Discount % = (Discount / MP) × 100
⚖️ Ratio & Proportion
- a : b = a/b, and if a : b = c : d → ad = bc
- Share Formula: (m / (m + n)) × Total
- Weighted Average: (Σ Quantity × Value) / Total Quantity
🕒 Time, Work & Distance
- Work = Rate × Time
- If A finishes in x days → 1/x work per day Combined (A + B) = (1/x + 1/y)
- Speed = Distance / Time
- Average Speed = (2xy) / (x + y)
💹 Interest & Investment
- SI = (P × R × T)/100
- CI = P(1 + R/100)^T – P
- ROI = (Gain or Loss / Investment) × 100
💼 Business & Ownership Math
| Concept | Formula / Meaning |
|---|---|
| Revenue Growth % | ((Current – Previous) / Previous) × 100 |
| Market Share % | (Company Sales / Total Market Sales) × 100 |
| Equity Split | Founder A : Founder B = Investment Ratio |
| Valuation (Basic) | ≈ Revenue × Industry Multiplier |
| Return on Investment (ROI) | (Profit / Investment) × 100 |
| Ownership after funding | New % = (Old Shares / Total Shares after funding) × 100 |
💡 Example: If you own 40% and issue new shares that double total shares → new ownership = (40 / 200) × 100 = 20%
🎲 Probability & Combinatorics
| Type | Formula | Example |
|---|---|---|
| Basic Probability | P(E) = Favourable / Total outcomes | Rolling even on dice = 3/6 = 0.5 |
| Independent Events | P(A and B) = P(A) × P(B) | Getting heads twice = (½ × ½) |
| Mutually Exclusive | P(A or B) = P(A) + P(B) | Drawing red or blue ball |
| Permutation | nPr = n! / (n–r)! | Arranging 3 out of 5 items |
| Combination | nCr = n! / [r!(n–r)!] | Selecting 3 out of 5 candidates |