Mathematics and Quantitative Aptitude
Syllabus shape
Percentage, ratio and proportion, average, profit and loss, simple and compound interest, time–work, speed–distance–time, HCF/LCM, mensuration, basic algebra, probability and data interpretation. Inspector papers are speed tests: 25–30 questions in 30–45 minutes.
Rules worth memorising
- Successive change: net % = a + b + ab/100, with signs.
- Profit % is on cost price; discount % is on marked price.
- SI = PRT/100; CI = P[(1 + R/100)^T − 1]; for two years the CI − SI gap = P(R/100)².
- Work: if A finishes in x days, one day's work = 1/x; combined rates add.
- Speed: distance = speed × time; km/h to m/s is ×5/18.
- Mean = sum ÷ count; for grouped data use class mid-values.
Worked example
A shopkeeper marks goods 40% above cost and allows 25% discount. Find profit %. Let cost = 100. Marked price = 140. Selling price = 140 × 0.75 = 105. Profit = 5 on 100, so 5%. Reasoning note: the two percentages sit on different bases, so they never cancel - do not subtract 25 from 40.
Traps
- Adding successive percentages directly (10% then 10% is 21%, not 20%).
- Computing profit on selling price when the question specifies cost price.
- Mixing units: metres with kilometres, minutes with hours.
- Rounding mid-calculation and then picking a near-miss option.