Numerical Ability: Unit Discipline and Standard Shortcuts
The paper tests speed on school-level arithmetic: number system, LCM/HCF, percentage, ratio, average, profit and loss, simple and compound interest, time-work, time-speed-distance, mensuration and data interpretation.
Methods that save time
- Successive percentage change: a% then b% gives a + b + ab/100.
- Speed conversion: km/h × 5/18 = m/s; convert before substituting.
- Time and work: take total work as the LCM of the given days and convert each rate to units per day.
- Average: total = average × count; adding one item changes the average by (new value − old average)/new count.
Worked example
A 150 m long train running at 54 km/h crosses a platform in 30 seconds. Find the platform length. Reasoning: 54 km/h = 54 × 5/18 = 15 m/s. Distance covered in 30 s = 15 × 30 = 450 m. That distance equals train plus platform: 150 + P = 450, so P = 300 m. Answer: 300 m.
Traps that cost marks
- Substituting 54 directly against 30 seconds without converting to m/s.
- Treating successive discounts of 20% and 20% as 40%; the correct figure is 36%.
- Computing profit or loss percentage on the selling price instead of the cost price.
- In compound interest, forgetting that year two earns interest on year one's interest.
- Ignoring the unit demanded in the question (metres or km, rupees or percent); one option always matches the unit error.
For data interpretation, read the axes and the legend before calculating, and use approximation only when the options are far apart.