Arithmetic and Numerical Ability
Syllabus and rules
Arithmetic and Numerical Ability tests speed with number system, percentages, ratio and proportion, averages, profit and loss, simple and compound interest, time and work, time and distance, mixtures, and data interpretation. Use exact fractions where possible and keep units consistent.
Core formulas
- Profit% = (SP − CP)/CP × 100; discount is always on marked price.
- SI = PRT/100; CI = P(1 + R/100)^T − P.
- Work: if A does a job in x days, one day's work is 1/x.
- Speed = distance/time; convert km/h to m/s by multiplying by 5/18.
- Average = sum of values/number of values.
Worked example
A trader marks an article 25% above cost and allows a 10% discount. Find profit%. Let CP = 100. MP = 125. Discount = 10% of MP = 12.50. SP = 112.50. Profit = 12.50 on CP 100, so profit% = 12.5%. The reasoning: the discount is calculated on the marked price, not on the cost price. A common wrong method takes 10% of 100 and gets 15% profit.
Traps
- Applying discount to CP instead of MP.
- Adding successive percentage changes directly; use multiplying factors.
- Mixing simple and compound interest for multi-year problems.
- Forgetting that time and work rates add only when people work together.
- Ignoring units in speed, work and interest questions.
Practice mental estimation to eliminate options, but show the exact step when two options are close.