Mathematics: Arithmetic, Mensuration, Basic Algebra and Geometry
Mathematics in Group D is speed-based arithmetic and mensuration with a little algebra and geometry. Accuracy in percentage, profit and loss, interest, averages, time–speed–distance and standard area/volume formulae covers most questions.
Core rules
- Profit and loss percentage is always calculated on cost price; discount is always calculated on marked price.
- Simple interest = PRT/100. Compound interest = P(1 + R/100)ᵀ − P.
- Speed = distance/time. A train crossing a pole travels its own length; crossing a platform travels length + platform.
- Average = sum of observations / number of observations.
- Areas: circle πr², triangle ½ × base × height, trapezium ½(a + b)h. Volumes: cylinder πr²h, cone ⅓πr²h, sphere (4/3)πr³.
- Pythagoras triplets worth memorising: 3-4-5, 5-12-13, 7-24-25.
Worked example
A shopkeeper marks an article 40% above cost and then allows a 25% discount. What is his profit percentage? Take CP = 100. Marked price = 140. Selling price = 140 × (75/100) = 105. Profit = 105 − 100 = 5, and profit percentage is on CP, so 5/100 × 100 = 5%. The reasoning step to remember is that the discount is applied to the marked price, not the cost price.
Traps
- Applying the discount to CP instead of MP - the most common error in this exact question type.
- Using SI logic for CI when the period exceeds one year.
- Substituting diameter where the formula needs radius.
- Forgetting to convert units (cm to m) before computing area or volume.