Quantitative Aptitude: Ratios, Rates and Data Interpretation
Quantitative Aptitude / Numerical Ability tests arithmetic fluency and interpretation under time pressure. Recurring areas are percentage, ratio, profit and loss, simple and compound interest, time-work, speed-distance, mixtures, number series, simplification, probability and data interpretation.
Core rules
- Convert percentages to fractions; successive percentage changes use a + b + ab/100.
- Simple interest is PRT/100; compound interest is P[(1 + r/100)^t - 1]. At simple interest, a sum doubles when r = 100/t.
- Time-work: combined rate is the sum of individual rates; efficiency is inversely proportional to time.
- In data interpretation, note the unit and base year before computing; form the required ratio before approximating.
Worked example
A sum doubles in 5 years at simple interest. Find the rate. Reasoning: let P = 100. The amount becomes 200, so simple interest is 100. Using SI = PRT/100: 100 = 100 × r × 5/100. Therefore r = 20% per annum. Do not use the compound-interest doubling rule here; at simple interest the growth is linear.
Traps that cost marks
Using the CI formula for an SI question; confusing percentage points with percent change; averaging speeds instead of using total distance divided by total time; ignoring 'approximately' in simplification; and misreading a DI table where one column is in lakh and another in crore. In number series, check differences, ratios and squares before assuming one pattern.