Mathematics - Arithmetic, Mensuration, Algebra and Geometry
What the paper expects
Quantitative aptitude here is speed-based: percentage, ratio and proportion, average, profit and loss, simple and compound interest, time–work, speed–distance, mensuration of standard solids, and basic algebraic identities plus elementary geometry (angles, triangles, circles).
Core formulae
- Profit per cent = (SP − CP)/CP × 100; discount is always on marked price.
- CI = P(1 + r/100)^n − P; SI = PRT/100.
- Work: if A finishes in x days and B in y days, together they take xy/(x + y) days.
- Speed = distance/time; average speed = total distance ÷ total time, never the average of speeds.
- Circle: area = πr², circumference = 2πr; cylinder volume = πr²h; sphere = 4/3πr³; cone = 1/3πr²h.
- Identities: (a + b)² = a² + 2ab + b²; a² − b² = (a + b)(a − b).
Worked example
A shopkeeper marks an article 40% above cost and allows a 15% discount. Find the profit per cent. Take CP = ₹100, so marked price = ₹140. Discount of 15% on ₹140 = ₹21, hence SP = ₹119. Profit = ₹19 on ₹100, so profit = 19%. Note that 40 − 15 = 25 would be wrong, because the discount applies to the marked price, not the cost.
Traps
Applying discount to cost price; averaging two speeds instead of dividing total distance by total time; forgetting unit conversion (metres to centimetres, minutes to hours); using diameter as radius; treating simple interest for multi-year compound interest questions.