Numerical Ability / Quantitative Aptitude
Numerical Ability / Quantitative Aptitude
This section tests arithmetic and mensuration: percentage, ratio, average, profit and loss, simple and compound interest, time-work, time-speed-distance, and areas and volumes. Accuracy under time pressure is the main challenge.
Core rules and concepts
- Percentage: successive changes of a% and b% give a + b + ab/100; use the correct base value.
- Profit/loss: profit% is on cost price unless "on selling price" is stated; discount is on marked price.
- Time and work: convert days to rates (1/n); combined rate is the sum; use LCM to avoid fractions.
- Speed: relative speed adds for opposite directions and subtracts for the same direction; trains must clear their own length plus the platform.
- Interest: SI = PRT/100; CI = P(1 + r/100)^t − P; for two years the CI−SI difference is P(r/100)².
- Mensuration: volume of cylinder πr²h, cone ⅓πr²h, sphere 4/3πr³; learn curved surface area formulas.
Worked example
A finishes a job in 12 days and B in 18 days. Working together, in how many days? Take LCM of 12 and 18 = 36 units. A does 3 units/day, B does 2 units/day, together 5 units/day. Time = 36/5 = 7.2 days.
Traps
Do not add days directly - rates add, not times. In train problems, convert km/h to m/s by multiplying by 5/18. In CI, do not use the SI formula for more than one year. In percentage, do not apply a discount to the selling price instead of the marked price.