Quantitative Aptitude
Quantitative Aptitude in FCI AG-III is a 20-question Phase I section (25 in Phase II) testing arithmetic rather than higher mathematics. Expect percentage, ratio and proportion, average, profit and loss, simple and compound interest, time and work, time-speed-distance, mixtures, mensuration, and data interpretation from tables, bar diagrams and pie charts.
Core rules and shortcuts
- Percentage change = (new − old)/old × 100. Successive percentage changes multiply: +20% then −10% gives 1.20 × 0.90 = 1.08, i.e. +8%, not +10%.
- For time and work, total work = rate × time. If A alone takes x days and B alone y days, together they take xy/(x + y) days.
- Profit percent is calculated on cost price unless the question says otherwise; discount percent is on marked price.
- SI = PRT/100. CI = P[(1 + R/100)^T − 1]. For two years, CI − SI = P(R/100)^2.
- Average = sum ÷ count. If a new entry equals the old average, the average is unchanged.
Worked example
A trader marks an article 40% above cost and allows successive discounts of 10% and 5%. Find the profit percent. Take CP = ₹100, so MP = ₹140. After 10% discount: 140 × 0.90 = ₹126. After 5%: 126 × 0.95 = ₹119.70. Profit = 119.70 − 100 = ₹19.70, so profit = 19.7%. The common error is adding discounts to 15% and computing 140 × 0.85 = ₹119, which gives 19% and is wrong because the second discount applies to the already reduced price.
Traps that cost marks
- Mixing SI and CI for periods over one year.
- Using SP instead of CP as the profit base.
- Forgetting unit conversion in speed questions (km/h to m/s: multiply by 5/18).
- In DI, reading the legend or scale incorrectly, or averaging percentages instead of totals.