Quantitative Aptitude: Percentages, Successive Change and Base Values
Quantitative Aptitude covers percentage, ratio and proportion, averages, profit and loss, simple and compound interest, time-work, time-speed-distance, mensuration and data interpretation. The marks sit in the arithmetic chapters, and almost every question can be attacked by assuming a convenient base value such as 100 rupees or 100 units.
Percentage and successive change
For two successive changes of a% and b%, the net change is a + b + ab/100, where a decrease is taken as negative. A 20 percent increase followed by a 20 percent decrease gives 20 minus 20 minus 4 = minus 4 percent, not zero.
Profit, loss and discount
Marked price is not cost price. Profit percent is always calculated on cost price unless the question says otherwise, and discount percent is always on marked price. Convert everything to one base: cost price 100, marked price 100 plus the markup, selling price = marked price times (1 minus discount/100).
Ratio, mixture and average
Equalise the number of parts before comparing ratios. In alligation, the ratio of quantities is the ratio of deviations from the mean. Average speed for equal distances is the harmonic mean, 2xy/(x+y), not (x+y)/2.
Time, work and speed
Work done is proportional to efficiency times days; efficiencies are in the inverse ratio of days taken. For trains, relative speed is the sum when moving opposite and the difference when moving in the same direction.
Worked example: a trader marks goods 40 percent above cost and allows a 25 percent discount. Take cost price = 100, so marked price = 140. Selling price = 140 times 0.75 = 105, giving a profit of 5 on 100, i.e. 5 percent.
Traps that cost marks
Applying discount on cost instead of marked price; applying profit percent on selling price; forgetting that compound interest changes the base every year; averaging two speeds arithmetically.