Mathematical Ability - Arithmetic: Ratios, Percentages, Interest, Work, Speed and Averages
Core toolkit
Arithmetic questions reward converting everything into ratios or fractions. Percentages: a 25% rise followed by a 20% fall returns to the original value, because 1.25 × 0.80 = 1. Successive discounts of a% and b% equal a single discount of a + b − ab/100.
Profit and loss: profit per cent is always on cost price unless the question says otherwise; marked price links to selling price through discount. Simple interest is linear in time; compound interest compounds annually unless stated half-yearly, in which case the rate is halved and the periods doubled.
Time and work: take total work as the LCM of the days given, convert each worker to units per day, then add or subtract. Filling and emptying pipes carry opposite signs. Time, speed and distance: distance is constant across a speed change, so time is inversely proportional to speed; for two trains, relative speed is the sum when opposite and the difference when same direction. Boats use downstream = b + s, upstream = b − s.
Average: total = average × count; when a member is replaced, the change in total equals the change in that member's value. Progressions: AP nth term a + (n − 1)d, sum n/2[2a + (n − 1)d]; GP nth term ar^(n − 1).
Worked example
Two successive discounts of 20% and 10% on ₹1,000. After the first, price = ₹800; after the second, 800 × 0.9 = ₹720. Total discount = ₹280, that is 28%, not 30%, because the second discount acts on the reduced price.
Traps
- Adding successive percentage changes instead of multiplying them.
- Computing profit per cent on selling price.
- Assuming CI equals SI beyond the first year.
- Using LCM work units but forgetting to convert back to days.