Numerical Ability: Speed Through Structure
What the section tests
Numerical Ability covers number system, HCF/LCM, percentages, profit and loss, ratio and proportion, averages, simple and compound interest, time-speed-distance, time and work, mensuration, and elementary algebra and geometry. The difficulty is moderate; the real constraint is time.
Concepts that carry the most marks
- Percentage as a multiplier: a 20% increase is ×1.2, a 20% decrease is ×0.8. Successive changes multiply.
- Ratio scaling for mixtures and partnership.
- Work-rate addition: combined rate = sum of individual rates; time = 1/rate.
- Relative speed for trains and boats (add for opposite direction, subtract for same direction).
- CI vs SI difference over two years = P(r/100)².
- Mensuration formulas for cylinder, cone, sphere and trapezium.
Traps to watch
- Percentage change applied to the wrong base (successive discounts are not additive).
- Mixing units - km/h with metres, minutes with hours.
- "Average" questions where a new member joins or leaves and the total changes.
- Options clustered around a common arithmetic slip; verify with approximation first.
Worked example
A shopkeeper marks an item 40% above cost and gives a 25% discount. Profit percent? Take cost = 100. Marked price = 140. Selling price = 140 × 0.75 = 105. Profit = 5%. Rule of thumb: fix the base at 100 whenever percentages are chained; the arithmetic becomes trivial and unit-free.