Mathematics (Quantitative Aptitude)
The quantitative paper is Class 10-level arithmetic under time pressure: number system, percentage, ratio and proportion, average, profit and loss, simple and compound interest, time–speed–distance, time and work, mensuration, and data interpretation from tables and bar charts. Speed comes from converting word problems into a single clean equation rather than from memorising shortcuts without understanding them.
Rules worth having at your fingertips
- Percentage change = (change ÷ original) × 100. Successive changes of a% then b% give a net effect of a + b + (ab ÷ 100).
- Profit and loss are always on cost price unless the question says otherwise; discount is always on marked price.
- Speed conversion: km/h to m/s multiply by 5/18; m/s to km/h multiply by 18/5.
- Time and work: if A alone takes a days and B alone b days, together they take ab ÷ (a + b) days.
- Simple interest = PRT ÷ 100; compound interest = P(1 + r/100)^t − P.
- Average = sum ÷ count; when one new item replaces an old one, the average shifts by the difference divided by the count.
Worked example
A shopkeeper marks an article 40% above cost price and allows a discount of 25%. Find his profit per cent. Reasoning: use the base-100 method. Let CP = ₹100, so MP = ₹140. A 25% discount means the selling price is 75% of the marked price: 140 × 75 ÷ 100 = ₹105. Profit = ₹5 on a cost of ₹100, so profit = 5%. Note that simply adding 40% and subtracting 25% to get 15% is wrong, because the discount applies to the marked price, not the cost price.
Traps that cost marks
- Applying a discount to cost price instead of marked price.
- Adding successive percentages instead of compounding them.
- Mixing metres and kilometres, or minutes and hours, inside one equation.
- Answering "approximately" when the question demands an exact value, or leaving the answer in the wrong unit.