Percentage — Concepts, Conversions and Exam-Ready Methods
Syllabus topic: Percentage, Ratio & Proportion, Square roots, Averages
Percentage is the single most reused idea in the SSC CGL Quant section: it appears directly as its own questions and hides inside Profit & Loss, Interest, and Data Interpretation. This note builds it from the definition up, so every later topic becomes easier.
What a percentage really is
Per cent means “out of every hundred”. Writing 37% is exactly the same as writing the fraction 37/100 or the decimal 0.37. Every percentage problem is therefore a fraction problem in disguise, and the candidates who convert quickly are the ones who finish the paper.
Memorise the common conversions until they are automatic: 1/2 = 50%, 1/3 = 33⅓%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16⅔%, 1/8 = 12½%, 1/10 = 10%, 1/11 = 9.09%, 1/12 = 8⅓%. When a question says “increased by 12½%”, thinking “increased by 1/8” lets you multiply by 9/8 in one step instead of doing long decimal arithmetic.
The three basic question shapes
Almost every direct question is one of three shapes: (1) find x% of a number — multiply; (2) a number is what percent of another — divide and multiply by 100; (3) after an increase or decrease of x%, find the new value — multiply by (100 ± x)/100. If you can classify a question into one of these shapes within seconds, the rest is arithmetic.
Successive changes do not add. A price raised 20% and then cut 20% does not return to the original: 100 → 120 → 96. The net effect of two successive changes of a% and b% is a + b + ab/100 percent. This one formula answers a large family of CGL questions on population growth, depreciation and double discounts.
- Net effect of successive changes a% and b% = a + b + (ab/100)%
- If A is x% more than B, then B is 100x/(100 + x)% less than A — the base changes, so the percentage changes
- For a fixed total spend, a price rise of x% forces a consumption cut of 100x/(100 + x)% to keep the budget unchanged
How to practise
Practise in layers: first pure conversions and the three basic shapes until they are error-free, then successive-change problems, then percentage inside DI tables. In the exam, never spend more than a minute on a percentage question — the concept is simple, so a stuck question is a reading problem, not a maths problem; mark it and return.
Key points to remember
- x% = x/100 — every percentage question is a fraction question.
- Learn the standard fraction ↔ percentage conversions by heart.
- Successive percentage changes combine as a + b + ab/100, never by plain addition.
- “A is x% more than B” and “B is x% less than A” are not symmetric — the base differs.
Topic from the official SSC CGL syllabus (Quantitative Aptitude / General Intelligence & Reasoning) as published in NaukriHelp's SSC CGL exam guide. Note written by NaukriHelp; standard mathematics references used for the subject only.