Mathematics: Arithmetic Shortcuts That Survive Exam Pressure
Core areas
The paper leans on percentage, ratio and proportion, average, profit and loss, simple and compound interest, time and work, speed and distance, mensuration, and data interpretation from tables and bar graphs.
Rules to keep ready
- Percentage change = (change ÷ original) × 100; always identify the base.
- Successive percentage changes multiply: a 20% rise then a 10% fall gives 1.20 × 0.90 = 1.08, not +10%.
- Time and work: convert days into rates (1/n per day), add rates, then invert the total.
- Compound interest = P(1 + r/100)^t − P; simple interest = PRT/100.
- Speed conversion: 1 km/h = 5/18 m/s.
Worked example
A shopkeeper marks an article at ₹1,500 and allows successive discounts of 20% and 10%. Find the selling price and the single equivalent discount. After 20%: 1500 × 0.80 = ₹1,200. After 10% on that: 1200 × 0.90 = ₹1,080. Total discount = 1500 − 1080 = ₹420. As a percentage, 420 ÷ 1500 = 28%. Shortcut check: 20 + 10 − (20 × 10)/100 = 30 − 2 = 28%. Both routes agree, so the selling price is ₹1,080 and the equivalent discount is 28%.
Traps that cost marks
- Adding discounts (30%) instead of multiplying them.
- Using the selling price as the base in a "profit on cost" question.
- Forgetting to convert minutes to hours in speed problems.
- Rounding in the middle of a calculation and then matching an option that is close but wrong.