Quantitative Aptitude for CAPF ASI (Stenographer)
Quantitative Aptitude checks numerical fluency across number system, percentage, ratio and proportion, average, profit and loss, discount, simple and compound interest, time and work, pipes and cisterns, speed–time–distance, mensuration and data interpretation. Most questions are solvable in under a minute with a shortcut, so learn formulas together with the situation each one applies to.
Core shortcuts
- Percentage change is always measured on the stated base; successive changes multiply. A 20% rise then a 20% fall leaves 0.96 of the original, a 4% loss.
- Profit and loss percentages are on cost price; discount is always on marked price.
- Work: convert each worker to one-day units; combined rate is the sum of rates.
- Average speed over equal distances is 2xy/(x+y), not (x+y)/2.
- Mensuration: circle area πr², circumference 2πr; cylinder volume πr²h; sphere volume 4/3πr³.
Worked example
A trader marks goods 40% above cost and allows a 25% discount. What is the profit percentage?
Reasoning: take CP = 100. Marked price = 140. Selling price = 140 × 0.75 = 105. Profit = 105 − 100 = 5, so 5%. Adding 40 − 25 = 15% is wrong because the discount applies to the marked price, not the cost price.
Traps that cost marks
- Applying discount to cost price instead of marked price.
- Using the arithmetic mean for average speed.
- Mixing units - minutes with km/h, or cm with m² in mensuration.
- In data interpretation, confusing "percentage of total" with "percentage more than".
- Rounding too early in multi-step calculations.