Quantitative Aptitude and Mathematics
Scope
Number system, HCF and LCM, percentages, ratio and proportion, averages, profit and loss, simple and compound interest, time-work, speed-distance (including train problems), mensuration and simple data interpretation. Most questions are one or two steps; the marks come from calculation discipline.
Formulae worth memorising
- Speed conversion: km/h × 5/18 gives m/s.
- Train crossing a pole: distance = length of train; crossing a platform: distance = train + platform length.
- Compound interest: A = P(1 + r/100)ⁿ; simple interest: SI = PRT/100.
- Work: if A finishes in x days and B in y days, together they take xy/(x+y) days.
- Circle area πr²; cylinder volume πr²h.
Worked example
A shopkeeper marks an article 40% above cost price and allows a 25% discount. Taking CP = ₹100, the marked price is ₹140 and the selling price is 140 × 0.75 = ₹105. Profit = ₹5 on ₹100, i.e. 5%. Note that the two percentages do not cancel - successive changes multiply, not add.
Traps
- Applying a percentage to the wrong base: discount is on marked price, profit is on cost price.
- Adding successive percentage changes (40% up then 25% down is 5% up, not 15%).
- Mixing simple and compound interest in two-year problems.
- Forgetting to convert units before dividing, or leaving answers in the wrong unit.
- In work problems, adding days instead of adding rates (1/x + 1/y).