Quantitative Aptitude: Shortcuts With a Check
What the section tests
Quantitative Aptitude / Numerical Ability covers simplification and approximation, number series, percentage, ratio and proportion, average, profit and loss, simple and compound interest, time-work, speed-distance, mensuration and data interpretation (table, bar, pie). The paper rewards accurate shortcuts, not long division.
Core rules
- Successive percentage change: changes of a% then b% give a net change of a + b + ab/100.
- Simple interest: SI = PRT/100. If a sum doubles in T years at SI, R = 100/T.
- Compound interest: A = P(1 + R/100)^T. For two years, CI − SI = P(R/100)².
- Ratio: convert every share to the same unit before splitting; in partnership, profit shares follow capital × time.
- Time and work: take total work as the LCM of the days given; efficiency is inversely proportional to time.
Worked example
A sum becomes ₹8,000 in 5 years and ₹9,200 in 7 years at simple interest. Find the principal and the rate. Interest for the 2 extra years = 9,200 − 8,000 = ₹1,200, so interest per year = ₹600. Interest for 5 years = ₹3,000, so principal = 8,000 − 3,000 = ₹5,000. Rate = (600 × 100)/5,000 = 12% per annum. Check: 5,000 + (5,000 × 12 × 5)/100 = 5,000 + 3,000 = 8,000. ✔
Traps that cost marks
Applying a percentage change to the wrong base (successive discount versus successive increase); mixing SI and CI formulas; forgetting that 'x% more than y' is not the same as 'y% less than x'; and reading a pie-chart slice as a raw number when the question asks for a percentage of the total. In series questions, test two interleaved patterns before assuming a single difference.