Quantitative Aptitude: Arithmetic Shortcuts and Data Interpretation
What the section tests
Numerical Ability for Scale II is arithmetic-heavy: percentage, ratio, averages, SI/CI, time-work, speed-distance, mixtures, and data interpretation. The paper expects fast approximation, but options often punish premature rounding.
Core rules
- Successive percentage change: net = a + b + ab/100, with signs.
- CI vs SI for 2 years: difference = P(r/100)^2. For 3 years: P(r/100)^2 × (300 + r)/100.
- Time-work: if A does 1/a and B 1/b per day, together 1/a + 1/b; time = ab/(a+b).
- Partnership profit shares follow capital × time, not capital alone.
- In DI, check whether the question asks for percentage of total, percentage change, or percentage points; these are different.
Worked example
A sum of ₹20,000 is invested at 10% per annum. Find the difference between CI and SI for 2 years. SI = 20,000 × 10 × 2/100 = ₹4,000. CI = 20,000[(1.10)^2 − 1] = 20,000 × 0.21 = ₹4,200. Difference = ₹200. Shortcut: 20,000 × (10/100)^2 = 20,000 × 0.01 = ₹200. Both methods agree; the shortcut is safe only for a 2-year horizon.
Traps
Do not use the 2-year CI−SI shortcut for 3 years; do not treat a 10% increase followed by a 10% decrease as zero (it is a 1% net fall); in time-work, do not add days directly when efficiencies differ; in DI, do not ignore 'approximately' when options are far apart.