Numerical Ability and Elementary Mathematics
Syllabus focus
Numerical Ability and Elementary Mathematics covers the number system, HCF and LCM, simplification, percentages, ratio and proportion, average, profit and loss, simple and compound interest, time–work, time–speed–distance, mensuration, and basic data interpretation. Class 10-level accuracy and speed matter.
Core rules
- Percentage change: an increase of x% followed by a decrease of y% is not x−y; multiply the factors (1+x/100)(1−y/100).
- Profit and loss are calculated on cost price unless the question states otherwise.
- Average = total sum divided by number of items; adding a value above the average raises the average by less than that value.
- Time–work: convert days to rates; combined rate = 1/a + 1/b.
- Mensuration: circle area πr², circumference 2πr; cylinder volume πr²h; keep units consistent.
Worked example
A price is increased by 25%. By what percentage must the new price be reduced to return to the original? Let the original price be ₹100. After a 25% rise it is ₹125. Required reduction = 25/125 × 100 = 20%. Shortcut: reduction % = increase/(100+increase) × 100 = 25/125 × 100 = 20%. The common wrong answer, 25%, assumes the reduction is calculated on the old price rather than the new one.
Traps that cost marks
- Charging discount and profit on the wrong base.
- Forgetting to convert minutes to hours in speed questions.
- Using diameter instead of radius in circle and cylinder formulas.
- Rounding too early in a multi-step calculation.
- Reading a ratio as a fraction without matching the order of terms.