Quantitative Aptitude and Data Interpretation: Percentages, Ratios and Duty Arithmetic
This domain tests numerical fluency under time pressure, with a customs flavour. Expect ratio and proportion, percentages and percentage change, averages and weighted averages, simple and compound interest, time-speed-distance, time and work, mixtures and alligation, and data interpretation from tables, bar and line charts, pie charts and caselets. In data interpretation the arithmetic is usually easy; the difficulty is choosing the right base and reading the chart accurately.
Core techniques
- Anchor conversions: 1/8 = 12.5 per cent, 1/16 = 6.25 per cent, 1/6 = 16.67 per cent, 3/8 = 37.5 per cent. Recognising these avoids long division.
- Successive percentage change: a change of a per cent followed by b per cent gives a + b + ab/100, a net effect, not a sum.
- Percentage change versus percentage points: moving from 4 per cent to 6 per cent is a rise of 2 percentage points, but a 50 per cent increase relative to the original rate.
- Weighted average: total value divided by total quantity, never the simple mean of two rates.
- Alligation: the ratio of two mixtures is the inverse of their deviations from the mean.
Worked example: landed cost
A consignment has an FOB value of USD 20,000, freight of USD 1,500 and insurance of USD 500, so the CIF value is USD 22,000. Customs duty is 10 per cent ad valorem: 0.10 x 22,000 = USD 2,200. Value added tax is 15 per cent charged on the CIF value plus duty: 0.15 x 24,200 = USD 3,630. Total border charge = 2,200 + 3,630 = USD 5,830, which is 26.5 per cent of CIF, not 25 per cent, because VAT is computed on a base that already includes duty.
Worked example: successive change
A duty rate rises 10 per cent and then falls 10 per cent. Net change = 10 + (-10) + (10 x -10)/100 = -1 per cent. The rate ends 1 per cent below where it started, not unchanged.
Data interpretation method
Read the axis units and the base year first; distinguish a value from a share; when asked for a share of a total, recompute the total rather than reading one slice. For caselets, convert every sentence into a number before computing.
Traps that cost marks
- Applying VAT to CIF only and forgetting to add duty to the base.
- Treating percentage points as a percentage change.
- Averaging rates instead of weighting by value or quantity.
- Mixing units such as thousands and lakhs within one table.
- Rounding intermediate results too early and drifting from the options.