Elementary Mathematics / Numerical Ability: Base, Rate, Units
What this section tests
Elementary Mathematics / Numerical Ability tests speed and accuracy on school-level arithmetic: number system, HCF–LCM, simplification, percentage, ratio and proportion, average, profit and loss, simple and compound interest, time–work, time–speed–distance, mensuration and data interpretation. The sums are easy; marks are lost to slow working and unit slips.
Core rules
- Percentage change: always measure the change against the original value; a rise from 40 to 50 is 25%, not 10%.
- Successive change: a% followed by b% equals a + b + ab/100.
- Profit and loss: profit% is on cost price unless stated otherwise, so selling price = CP x (100 + profit%)/100.
- Time and work: convert days into per-day rates (1/n) before adding; combined rate is the sum of individual rates.
- Speed: 1 km/h = 5/18 m/s; for a train crossing a platform, total distance = train length + platform length.
Worked example
A candidate scoring 40% fails by 30 marks, while 55% gives 30 marks more than the pass mark. Find the maximum marks. The two scores differ by 55% − 40% = 15% of the maximum, and that gap equals 30 + 30 = 60 marks. So 15% of M = 60, giving M = 400. Check: 40% of 400 = 160 and the pass mark is 190; 55% of 400 = 220 = 190 + 30. Answer: 400.
Traps that cost marks
- Applying a percentage to the new value instead of the base value.
- Mixing minutes with hours or centimetres with metres mid-calculation.
- In data interpretation, reading the wrong row or ignoring the axis scale.
- Rounding too early; keep fractions until the final step, then round.