Arithmetic / Elementary Mathematics
Arithmetic is the highest-scoring section for a prepared candidate because question types repeat: percentage, profit and loss, ratio, average, simple and compound interest, time and work, time and distance, mensuration and data interpretation. Speed comes from formula recall plus disciplined approximation.
Formula deck
- Profit per cent = profit / cost price × 100; selling price = cost price × (1 + p/100).
- Discount is always calculated on the marked price; profit is always on the cost price.
- Simple interest = P × r × t / 100; compound interest = P[(1 + r/100)^t - 1].
- For two years, the gap between CI and SI equals P(r/100)².
- Work: if A finishes in a days and B in b days, together they take ab/(a + b) days.
- Speed: 1 km/h = 5/18 m/s; distance = speed × time.
Worked example
A shopkeeper marks an article at ₹800, allows a 25% discount, and still makes a 20% profit. Find the cost price. The selling price is 800 × 0.75 = ₹600. Since ₹600 is 120% of cost, cost = 600 / 1.2 = ₹500. The reasoning step that saves time is separating the two bases: discount acts on the marked price, profit on the cost price. Candidates who take 20% of ₹800 get a wrong figure.
Where marks are lost
Applying the profit percentage to the selling price, adding successive discounts instead of compounding them (two successive 10% discounts give 19%, not 20%), and forgetting unit conversion in speed questions.
Practice design
Run short timed sets of ten questions per topic and keep an error log tagging each mistake as conceptual or arithmetic; re-solve only the logged questions after a week.