Aptitude and Mental Ability
Scope
Aptitude and Mental Ability tests numerical competence under time pressure: percentages, ratio and proportion, averages, profit and loss, simple and compound interest, time–work, speed–distance, mensuration, and data interpretation, plus mental ability items such as number series and mirror or water images.
Core formulas
- Percentage change = (change ÷ original) × 100; successive changes multiply, not add: +20% then −20% gives 0.96 of the original, a 4% fall.
- Average speed for equal distances = 2xy/(x+y), not (x+y)/2.
- Simple interest = PRT/100; compound interest = P[(1+R/100)^T − 1].
- Time–work: if A finishes in x days and B in y days, together they take xy/(x+y) days.
- Train crossing a platform: total distance = train length + platform length.
Worked example
A train 120 m long runs at 54 km/h and crosses a 180 m platform. Convert speed: 54 × 5/18 = 15 m/s. Total distance = 120 + 180 = 300 m. Time = 300 ÷ 15 = 20 seconds. Reasoning: the engine must clear the platform, so the train’s own length is added.
Traps
- Mixing km/h and m/s; multiply by 5/18, not 18/5.
- Adding successive percentage changes instead of multiplying factors.
- Using the arithmetic mean for average speed over equal distances.
- In time–work, adding days instead of adding rates (1/x + 1/y).
- Ignoring units in mensuration (cm² versus m²).