Arithmetic: Percentages, Interest and Rate Problems
The Arithmetic section tests numerical ability under time pressure: simplification, percentages, ratio and proportion, averages, profit and loss, simple and compound interest, time–work, time–speed–distance, mensuration and data interpretation. Most questions are built from two or three standard formulas, so recognising the model matters more than long calculation.
Core formulas
- Successive percentage change: net effect = a + b + ab/100, with discounts taken as negative.
- Simple interest = P × R × T / 100; amount = P(1 + RT/100).
- Compound interest amount = P(1 + R/100)^T; for two years the CI–SI difference is P(R/100)².
- Work: if A finishes in x days and B in y days, together they take xy/(x + y) days.
- Speed: distance is constant, so time is inversely proportional to speed.
Worked example
A sum doubles in 8 years at simple interest. In how many years will it become four times? Reasoning: doubling means the interest earned equals the principal, so 100% interest accrues in 8 years and the rate is 12.5% per annum. To become four times, interest must equal three times the principal, i.e. 300%. At 100% per 8 years, 300% needs 8 × 3 = 24 years. Answer: 24 years.
Traps that cost marks
- Applying compound interest where simple interest is specified, or using the CI–SI difference formula beyond two years.
- Percentage change is always measured on the base stated in the question - a rise from 40 to 50 is a 25% rise, not 10%.
- 'By what percent' versus 'what percent' - the denominator differs.
- Mixing units in speed problems (km/h with metres and seconds).
- Rounding too early in data interpretation; carry fractions to the last step.