Mathematics and Quantitative Aptitude
Mathematics and Quantitative Aptitude tests arithmetic speed and accuracy: percentages, ratio and proportion, averages, profit and loss, simple and compound interest, time–speed–distance, time and work, mixtures, and data interpretation.
Core rules
- Percentage change is always calculated on the original base unless the question states otherwise.
- Successive percentage changes multiply: a 20% increase followed by a 10% decrease gives 1.20 × 0.90 = 1.08, a net 8% increase.
- Average speed for equal distances is the harmonic mean: 2xy/(x+y), not (x+y)/2.
- Simple interest is P × R × T / 100; compound interest uses P(1 + R/100)^T.
- In ratio problems, assign a common multiplier k and convert every quantity to the same unit.
Worked example
A jacket marked at ₹1,000 gets successive discounts of 20% and 10%. After the first discount: 1,000 × 0.80 = ₹800. The second discount applies to ₹800, not ₹1,000: 800 × 0.90 = ₹720. Total discount = ₹280, so the single equivalent discount is 28%. Adding 20% + 10% = 30% overstates the discount because the second percentage has a smaller base.
Traps
- Adding successive discounts or mark-ups instead of multiplying factors.
- Assuming a 20% increase and 20% decrease cancel out; they give a 4% net decrease.
- Using the arithmetic mean for average speed over equal distances.
- Forgetting to convert minutes to hours in speed questions.
- Reading data-interpretation tables without checking units and totals.
Practise with a calculator-free timing drill and write the base for every percentage change.