Quantitative Aptitude & Numerical Ability: Arithmetic Shortcuts
What the numerical paper tests
Quantitative Aptitude & Numerical Ability in Tier-I is arithmetic-heavy: number system, HCF–LCM, percentages, ratio and proportion, averages, profit and loss, simple and compound interest, time–speed–distance, time and work, ages, mensuration, basic trigonometry, simplification and approximation, and data interpretation.
Formulas to keep at your fingertips
- Percentage change = (change ÷ original) × 100.
- Profit% and loss% are calculated on cost price; discount% on marked price.
- SI = PRT/100; CI = P(1 + r/100)^t − P; for two years the CI–SI gap is P(r/100)².
- Time and work: if A finishes in a days and B in b days, together they take ab/(a+b) days.
- Speed = distance ÷ time; km/h → m/s means multiplying by 5/18.
- Circle area = πr²; cylinder volume = πr²h; sphere volume = (4/3)πr³.
Worked example
A trader marks his goods 40% above cost and allows a 25% discount. What is his profit? Take cost price = 100. Marked price = 140. Selling price = 140 × 0.75 = 105. Profit = 105 − 100 = 5, that is 5%.
Traps that cost marks
Applying a percentage to the wrong base; treating successive discounts as a simple sum (20% then 10% is 28%, not 30%); using simple-interest logic in compound-interest questions; forgetting unit conversions in speed problems; and rounding too early in approximation questions.