Mathematics and Quantitative Aptitude
What this domain tests
Percentages, ratio and proportion, averages, profit and loss, simple and compound interest, time-speed-distance, time and work, mixtures, mensuration and data interpretation. Speed with clean arithmetic matters more than advanced theory.
Core rules
- Successive percentage change: net = a + b + ab/100, with signs negative for a decrease.
- Profit and loss: discount is always calculated on marked price; profit percentage is always on cost price unless stated otherwise.
- Compound interest: for two years the difference between CI and SI equals P(r/100)².
- Time and work: convert days to units of work per day, then add rates; two people together take xy/(x+y) days.
- Speed conversion: km/h × 5/18 = m/s.
- Average: sum = average × number of items; adding a value above the average raises the average by (value − average)/new count.
Worked example
A trader marks goods 40% above cost and then allows a 25% discount. Find the profit percentage. Take cost price = ₹100. Marked price = ₹140. Discount = 25% of 140 = ₹35. Selling price = ₹105. Profit = ₹5 on ₹100, so 5%. The reasoning matters: the discount applies to the marked price, not the cost price. A common wrong route is 40 − 25 = 15% profit, which ignores that 25% of a larger marked price is more rupees than 25% of cost.
Worked example 2 (percentages)
A salary rises 20% and then falls 10%. Net change = 20 + (−10) + (20 × −10)/100 = 10 − 2 = 8% increase.
Traps that cost marks
Applying discount on cost price; treating simple interest as compounding; forgetting unit conversion in speed problems (minutes to hours); misreading 'successive' discounts as a single sum; in data interpretation, missing the unit written in the table caption (lakh tonnes vs thousand tonnes).