Study Guide · Chapter 15
3.15 Common Mistakes Aspirants Make
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- Using the wrong base for “increase/decrease” calculations. The original (initial) value is always the denominator — never the new value. “A is 20% more than B” does NOT mean “B is 20% less than A”; the correct figure is 16.67% (see Section 3.5). A student who answers “20%” here has computed the difference as a percentage of B instead of A.
- Sign errors in the successive percentage change formula. A decrease must be entered as a negative number in a + b + ab/100. Forgetting the negative sign on the “ab/100” cross-term (which can flip sign twice) is a very frequent slip — always write out a and b explicitly with their signs before substituting. For “decrease 20%, decrease 10%,” writing ab/100 as +2 instead of correctly computing (−20)×(−10)/100 = +2 by explicit sign multiplication often leads to arithmetic confusion when one of the two changes is itself negative twice over in a chained problem.
- Assuming “increase by x% then decrease by x%” gives a net zero change. It never does — it always results in a net decrease of x²/100 % (Section 3.14, Trick 4). A ₹100 item that rises 50% to ₹150 and then falls 50% lands at ₹75, not back at ₹100 — a 25% net loss, exactly matching 50²/100 = 25.
- Treating “percentage point difference” and “percentage change” as the same thing. A change from 20% to 25% is a 5 percentage-point rise but a 25% relative increase (since 5/20 × 100 = 25%) — these numbers are both valid answers to different questions, and misreading which one is being asked costs marks.
- Forgetting to remove invalid votes before splitting an election’s vote share. Candidate percentages in election problems are almost always percentages of valid votes, not of total voters — always compute the valid vote pool first, then apply each candidate’s share to that smaller pool, not to the original total voter count.
- Rounding fraction-table values too early or too crudely. Using “33%” instead of “33.33%” (i.e., 33⅓%) for 1/3 introduces cumulative error in multi-step problems; when precision matters, carry the exact fraction (1/3, 2/3, 1/6, etc.) rather than the rounded decimal until the final step, especially in successive-change or DI-table calculations where small rounding errors compound.
- Misidentifying the base in ratio-to-percentage conversion. For a ratio a : b, the whole is (a + b), not a or b alone — a common error is computing a/b × 100 instead of a/(a+b) × 100. For a 3:5 ratio, the first part’s share of the whole is 3/8 = 37.5%, not 3/5 = 60%.
- Confusing pass marks as a percentage of the “marks obtained” instead of the “maximum marks.” Pass percentage is always of the total maximum marks for that paper/subject, not of any candidate’s score — setting up the equation as (pass%) × (candidate’s marks) instead of (pass%) × (maximum marks) is a frequent algebra-setup error.
- In reverse-percentage problems, subtracting instead of dividing. If a final value V resulted from a p% increase on an unknown original, students often incorrectly compute V − p% of V; the correct method is to divide V by (1 + p/100), since the p% was of the original, not of V. Subtracting p% of V from V systematically under- or over-corrects and gives a wrong original value.
- Ignoring compounding in multi-year population/depreciation problems. Each year’s percentage change applies to the previous year’s value, not the original value — using simple addition/subtraction of percentages across years (rather than successive multiplication) is a very common and costly error. Two years of 10% growth is NOT a flat 20% increase; it is (1.1)² − 1 = 21% increase.
- Forgetting that “percentage” figures above 100% are valid and sometimes required. If this year’s production is 250% of last year’s, that means production is 2.5 times last year’s figure, not an “impossible” number — many aspirants freeze or second-guess themselves when a computed percentage exceeds 100%, when in fact this is entirely normal whenever the part being measured is larger than the base.
- Applying the price–consumption constant-expenditure formula in the wrong direction. Using r/(100+r) when the price has decreased (it should be r/(100−r) for a decrease), or vice versa, silently swaps the two mirror formulas from Section 3.7 and produces an answer that is numerically plausible but wrong — always re-confirm from the question whether price rose or fell before selecting which denominator to use.
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