Mathematics / Numerical Ability: Arithmetic Under Time Pressure
The mathematics block is Class 8–10 arithmetic. Speed matters more than depth: with a large paper and a short window, you need about a minute per question and a habit of approximating.
High-yield topics
- Percentage and its applications: profit-loss, discount, simple and compound interest, population change.
- Ratio-proportion, partnership, mixtures and alligation.
- Average, including weighted averages.
- Time-work and pipes-cisterns; time-speed-distance, trains and boats.
- Number system: divisibility rules, LCM-HCF, remainders.
- Mensuration: area and perimeter of triangles, circles, rectangles; volume of cylinder, cone, sphere; plus table and bar-chart interpretation.
Worked example
A trader marks an article 40% above cost and allows a 25% discount. Find the profit per cent. Take cost = ₹100. Marked price = ₹140. Discount = 25% of 140 = ₹35, so selling price = ₹105. Profit = ₹5 on ₹100, i.e. 5%. The trap is computing 40 − 25 = 15%. A discount applies to the marked price, not the cost, so chained percentages must be applied step by step on the changing base.
Safe shortcuts
- Successive change of a% then b%: net = a + b + ab/100.
- Cost of x articles equals selling price of y articles: profit% = (x − y)/y × 100.
- Equal distances at speeds x and y: average speed = 2xy/(x+y), never (x+y)/2.
- CI − SI for two years = P(r/100)².
Traps
- Mixing SI and CI beyond one year.
- Wrong base in 'B is what per cent more than A' versus 'A is what per cent less than B'.
- Unit mismatch: km/h with minutes, centimetres with metres.
- Over-computing when options are far apart - approximate and move on.