Elementary Mathematics and Quantitative Aptitude
Elementary Mathematics and Quantitative Aptitude tests arithmetic and basic mensuration: number system, HCF/LCM, percentages, ratio and proportion, averages, profit and loss, simple and compound interest, time–work, speed–distance, and areas/volumes. The questions are usually direct; marks are lost to unit and base errors.
Core rules
- Percentage change: use a base of 100 for cost price or original value.
- Profit/loss: profit% is always on cost price unless stated; discount is on marked price.
- Successive changes: net change = a + b + ab/100, with signs.
- Time–work: convert days to work per day; combined rate = sum of individual rates.
- Speed–distance: convert km/h to m/s by multiplying by 5/18.
Worked example
A shopkeeper marks an article 40% above cost and allows a 25% discount. Find the profit percentage. Take CP = ₹100. Marked price = ₹140. Discount = 25% of 140 = ₹35. Selling price = 140 − 35 = ₹105. Profit = 105 − 100 = ₹5, so profit% = 5/100 × 100 = 5%. The trap is calculating 25% of cost instead of marked price.
Traps
- Taking discount on CP rather than MP.
- Adding successive percentages directly (10% + 10% ≠ 20%).
- Mixing km/h and m/s in the same problem.
- Using diameter instead of radius in area/volume.
Key points
- Set CP or original value to 100 in percentage problems.
- Keep profit base and discount base separate.
- Use the net-change formula for two successive changes.
- Convert units before calculating speed or mensuration.
- Check whether interest is simple or compounded annually.