Quantitative Aptitude · Arithmetic
Percentage — the shortcuts that save time
7 min read
Percentage increase and decrease, successive change, and the fraction equivalents worth learning by heart.
Percentage questions are almost free marks once the basics are automatic — and they are the single biggest source of careless errors under time pressure.
The one mistake that costs most marks: percentage change is always measured against the ORIGINAL value, not the new one. If a price rises from ₹80 to ₹100, the increase is ₹20 on a base of ₹80, so 20/80 = 25%. Dividing by 100 gives 20%, which is the answer examiners deliberately include as a distractor.
Fraction equivalents worth knowing instantly: 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16.67%, 1/7 = 14.28%, 1/8 = 12.5%, 1/9 = 11.11%, 1/10 = 10%, 1/11 = 9.09%, 1/12 = 8.33%.
Converting a percentage to a fraction turns multiplication into cancellation and is usually faster than decimals.
Successive percentage change. Applying +a% then +b% is not (a+b)%. The net change is: a + b + (ab/100)
So a 10% rise followed by a 10% fall is 10 − 10 − 100/100 = −1%, a net 1% loss, not zero. Use negative values for decreases.
If a value increases by x%, the reduction needed to return to the original is: (100x) / (100 + x) %
And if a quantity's price rises by x%, consumption must fall by that same expression to keep expenditure unchanged. That single formula covers a large family of questions.