Mathematics: Arithmetic Speed with Clean Formulas
Mathematics is the most time-efficient section when the formulas are automatic. The paper leans on arithmetic - percentage, ratio and proportion, average, profit and loss, simple and compound interest, time–work, time–speed–distance - plus mensuration, elementary algebra and basic geometry (angles, triangles, circles).
Core rules
- Percentage change = (change ÷ original) × 100. Two successive changes of a% and b% give a + b + (ab ÷ 100).
- Profit and loss percentages are always on cost price; discount is always on marked price.
- SI = PRT ÷ 100; CI = P(1 + R/100)^T − P.
- Work: a worker finishing a job in x days does 1/x of it per day; combined rates add, and days = reciprocal of the combined rate.
- 1 km/h = 5/18 m/s; 1 hectare = 10,000 m².
Worked example
A shopkeeper marks an item 40% above cost and allows a 25% discount. Find his profit per cent. Reasoning: take CP = ₹100, so marked price = ₹140. The discount is on the marked price: 25% of 140 = 35, giving SP = ₹105. Profit = 105 − 100 = ₹5, and profit per cent on CP = 5%. The tempting wrong route applies 25% to the cost price, which produces a false 15%.
Traps that cost marks
- Computing discount on cost price, or profit on selling price.
- Adding successive percentage changes instead of compounding them.
- Missing unit conversion in speed and area questions.
- In work problems, correctly finding the rate and then forgetting to invert it to get days.
- In average questions, changing one value and re-averaging only the change rather than the new total.