Mathematics & Reasoning
Numerical ability covers percentage, ratio and proportion, average, profit and loss, simple and compound interest, time–speed–distance, time and work and the number system; reasoning covers series, coding–decoding, blood relations, direction sense, syllogism, analogies and seating arrangement.
Rules worth memorising
- Successive percentage changes of a% then b% give a + b + ab/100.
- Profit after markup m and discount d: (1 + m/100)(1 − d/100) − 1.
- 1 m/s = 18/5 km/h; average speed = total distance ÷ total time, never the mean of two speeds.
- If A finishes work in x days and B in y days, together they take xy/(x+y) days.
Worked example
A trader marks an item 40% above cost and allows a 25% discount. Find the profit. Reasoning: take cost = ₹100, so marked price = ₹140. Selling price = 140 × 0.75 = ₹105. Profit = ₹5 on ₹100 = 5%. The tempting answer, 15%, is wrong because the discount is calculated on the marked price, not on the cost.
Traps
- Treating markup and discount as independent percentages that simply cancel.
- Forgetting unit conversion: minutes to seconds, metres to kilometres, before applying speed formulae.
- In syllogism, accepting a conclusion that is merely possible; only conclusions true in every case count.
- In blood relations, losing track of gender - mark M or F beside each name.
- In direction sense, assuming a left turn is always west; sketch each turn from the current facing.