Arithmetic and Numerical Ability
Arithmetic and Numerical Ability tests school-level numerical competence: number system, HCF and LCM, percentage, ratio and proportion, average, profit and loss, simple and compound interest, time and work, speed and distance, mensuration, and data interpretation. Speed comes from choosing the shortest valid method and keeping units consistent.
Core rules
- Percentage change: use multiplying factors; a 20% increase is ×1.20, a 20% decrease is ×0.80.
- Profit and loss: profit percent is on cost price unless stated; discount is on marked price.
- Successive changes: the net factor is the product of individual factors, not their sum.
- Time and work: convert days to rates; if A does work in x days, A’s rate is 1/x per day.
- Speed: distance = speed × time; convert km/h to m/s by multiplying by 5/18.
Worked example
A shopkeeper marks an article 25% above cost and allows a 10% discount. Find profit percent. Reasoning: Let cost price = 100. Marked price = 125. After a 10% discount, selling price = 125 × 0.90 = 112.50. Profit = 112.50 − 100 = 12.50, so profit percent = 12.5%. Shortcut: 1.25 × 0.90 = 1.125, which is 12.5% profit.
Traps
- Calculating discount on cost price instead of marked price.
- Adding successive percentage changes instead of multiplying.
- Mixing simple and compound interest, or applying a compound formula without checking the period.
- Forgetting unit conversion in speed or mensuration problems.
- Rounding too early and choosing an option that differs by a small amount.