Numerical Ability and Elementary Mathematics
Topics
Simplification, number system, HCF and LCM, percentage, ratio and proportion, average, profit and loss, simple and compound interest, time and work, speed–distance–time, mensuration and elementary data interpretation.
Formulas to hold
- Percentage change = (change ÷ original) × 100.
- Profit% = profit ÷ CP × 100; SP = CP × (100 + profit%) ÷ 100.
- SI = PRT ÷ 100; CI = P(1 + R/100)^T − P.
- Work: if A finishes in x days, one day’s work is 1/x, and combined rates add.
- Speed: km/h to m/s multiply by 5/18; m/s to km/h multiply by 18/5.
Worked example
“A shopkeeper buys at ₹800, marks up 25%, then gives a 10% discount. Find the profit percentage.” Marked price = 800 × 1.25 = ₹1000. Selling price = 1000 × 0.90 = ₹900. Profit = ₹100 on ₹800, which is 12.5%. Shortcut: 1.25 × 0.90 = 1.125, so the profit is 12.5%.
Traps that cost marks
- Applying the discount to cost price instead of marked price.
- Using the simple interest formula for compound interest; for two years the difference is P(R/100)².
- Adding successive percentage changes instead of multiplying them.
- Confusing average speed (total distance ÷ total time) with the mean of two speeds.
- Forgetting that HCF × LCM = product of the two numbers.