Mathematics and Quantitative Aptitude: Arithmetic Shortcuts and Formula Recall
What is tested
Simplification, percentage, ratio and proportion, average, profit and loss, simple and compound interest, time and work, time–speed–distance, mensuration of squares, rectangles, circles and triangles, plus a small data-interpretation table or bar chart. Speed matters: most items are designed to be solved in under a minute with the right formula.
Formulas to have ready
- Successive change: multiply factors, never add them.
- CI for 2 years = P(1 + r/100)²; the gap between CI and SI for 2 years = P(r/100)².
- Profit% and loss% are on cost price unless the question says otherwise.
- Replacing one value: new average = old average + (new value − old value)/n.
- Work: if A alone takes a days and B alone b days, together they take ab/(a+b) days.
- Speed: km/h to m/s is × 5/18; relative speed adds for opposite directions, subtracts for the same direction.
Worked example
A clerk's salary is raised by 20% and then cut by 10%. What is the net change? Take the original as 100. After the rise: 120. After the cut: 120 × 0.90 = 108. Net change = 108 − 100 = 8, so a rise of 8% - not 10%.
Traps
- Adding successive percentages (+20 − 10 = +10) instead of multiplying.
- Computing profit on selling price when cost price is the stated base.
- Averaging the averages of unequal groups without weighting by group size.
- Skipping unit conversion in speed questions, or mixing metres and centimetres in mensuration.