Arithmetical and Numerical Ability: Core Calculations
What the domain tests
Arithmetical and Numerical Ability tests school-level computation and its application: number system, LCM/HCF, percentage, ratio and proportion, average, profit and loss, simple and compound interest, time–work, speed–distance, mensuration and data interpretation. The JE paper expects accuracy with fractions and unit conversions more than advanced theory.
Core rules
- Percentage: always identify the base. A 20% increase followed by a 20% decrease gives 0.8 × 1.2 = 0.96, a 4% net fall, not zero.
- Time–work: convert days to one-day work. If A takes 12 days and B takes 18, their rates are 1/12 and 1/18.
- Profit/loss: profit% is on cost price unless stated otherwise; discount% is on marked price.
- CI: A = P(1 + r/100)^n; SI = PRT/100. For two years, CI − SI = P(r/100)^2.
- Mensuration: keep all dimensions in the same unit before substituting.
Worked example
A can finish a job in 12 days, B in 18 days. How long together? LCM of 12 and 18 is 36 units of work. A does 3 units/day, B does 2 units/day; together 5 units/day. Time = 36 ÷ 5 = 7.2 days, i.e. 7 days 4.8 hours. Answer: 7.2 days.
Traps
Adding times instead of rates; applying profit% to selling price; using SI for CI; forgetting that successive discounts of 10% and 20% equal 28%, not 30%; and in DI, answering from a row rather than the asked column.