Mathematics and Quantitative Aptitude - Arithmetic Rules and Worked Reasoning
This domain tests the arithmetic a vocational student actually meets: costing, measurement, and simple data handling. Expect number operations, percentage, ratio and proportion, average, profit and loss, interest, time and work, mensuration, and interpretation of small tables.
Core rules
- Percentage change is always calculated on the base named in the question; successive changes multiply rather than add.
- Profit and loss are calculated on cost price (CP); discount is calculated on marked price (MP).
- Simple interest: SI = P × R × T / 100. Compound interest: CI = P(1 + R/100)^T − P.
- Average = total of values ÷ number of values; in a weighted average, multiply each value by its weight first.
- Unitary method: fix the rate for one unit, then scale up or down.
- Mensuration: area of a circle = πr², circumference = 2πr; volume of a cylinder = πr²h; 1 m³ = 1000 litres.
Worked example
A shopkeeper buys an item for ₹400, marks it 25% above cost, and allows a 10% discount. Find the profit percentage.
- MP = 400 × 1.25 = ₹500.
- Discount is on MP: SP = 500 × 0.90 = ₹450.
- Profit = 450 − 400 = ₹50; profit % = 50 ÷ 400 × 100 = 12.5%. Note the reasoning: if you had taken 10% of ₹400, you would get ₹440 and a wrong answer of 10%.
Traps that cost marks
- Computing discount on CP instead of MP.
- Mixing units: cm² to m² is ÷10,000, not ÷100.
- Treating time-and-work as direct proportion - more workers mean fewer days.
- Forgetting that CI exceeds SI by the interest earned on interest.
- Including or excluding a member from an average without adjusting the count.