Percentage Questions for SSC CGL

Basic Concept and Conversion

Percent means per hundred. When you say 35%, you mean 35 out of every 100. Converting between fractions, decimals, and percentages is the first skill SSC tests indirectly in DI and comparison questions. Memorising key fraction-to-percent conversions saves 20-30 seconds per question.

• x% of y = (x/100) x y
• To convert fraction to percent: multiply by 100
• 1/8 = 12.5%, 1/6 = 16.67%, 1/7 = 14.28%, 3/8 = 37.5%
• 1/3 = 33.33%, 2/3 = 66.67%, 3/4 = 75%, 4/5 = 80%
• If A is x% of B, then B is [100/x x 100]% of A — this reverse is heavily tested

Percentage Increase and Decrease

SSC CGL loves asking how much something increased or decreased relative to its original value. The original value is always the base (denominator). A common trap is using the new value as base — always anchor to the original value unless told otherwise.

• Percentage increase = [(New - Old) / Old] x 100
• Percentage decrease = [(Old - New) / Old] x 100
• If price increases by x%, then to restore original: decrease by [x/(100+x)] x 100%
• If price decreases by x%, then to restore original: increase by [x/(100-x)] x 100%
• These restore formulas appear almost every year — memorise them

Successive Percentage Change

When a value changes by two percentages one after another — like two consecutive discounts, or population growing for 2 years — you cannot simply add the percentages. SSC CGL tests this in DI, population, and shopkeeper problems. The net effect formula solves this in one step.

• Net effect of two changes a% and b% = a + b + (ab/100)%
• If both are increases, ab is positive, so net > a+b
• If one is increase and other decrease, treat decrease as negative
• If both are decreases, the formula still works with negative signs
• Three successive changes: apply formula twice

Income, Expenditure, Savings Model

A favourite SSC pattern: Income increases/decreases by x%, expenditure increases/decreases by y%, find change in savings. Or: If income and expenditure are given as percentages of each other, find savings. Always define savings = Income minus Expenditure and track each component.

• Savings = Income - Expenditure
• Assign a base value (say Income = 100) to avoid fractions
• If income rises 10% and expenditure rises 15%, calculate new savings and compare
• Questions often give expenditure as % of income — find absolute expenditure first
• Percentage change in savings can be very large even for small changes in income/expenditure

Population and Depreciation

These follow compound-style percentage formulas. Population grows at r% per year, find population after n years. Depreciation problems use the same structure but with decrease. SSC often asks for population after 2-3 years or working backwards to find original population.

• Population after n years = P x (1 + r/100)^n
• Depreciation after n years = P x (1 - r/100)^n
• For 2 years, expansion is faster than simple addition of r% twice
• Use successive change formula for 2-year problems to save time
• If final population given, divide back using the same formula

• Using new value as base instead of original value when calculating percentage change — always anchor to old/original
• Adding percentage changes directly: 10% up then 10% down is NOT zero, it is -1% due to the ab/100 term
• Forgetting to take the restore formula — if price increased by 20%, required decrease is 16.67% not 20%
• In income-expenditure problems, calculating % change in savings incorrectly by ignoring that savings is a small difference of two large numbers
• Misreading 'A is 25% more than B' as 'B is 25% less than A' — they are NOT the same. If A = 1.25B, then B = A/1.25 = 80% of A, so B is 20% less than A

• BORN trick for restore: Base is Old, Reduce by New denominator. After 25% rise (base 125), reduce = 25/125 = 20%
• Successive change shortcut: think of it as (100+a)(100+b)/100 - 100. Two negatives give small positive ab term, opposite signs give negative ab term.
• Fraction flashcard order: 1/8=12.5, 1/6=16.67, 1/5=20, 1/4=25, 1/3=33.33, 1/2=50. Double the numerator to double the percent.
• SAY IT formula for savings: S = I - E. Assign I = 100 always when no absolute values given. Saves calculation time.

• SSC CGL Tier 1 typically has 2-3 direct percentage questions plus 3-5 indirect ones inside DI sets — so effective weightage is very high
• The restore percentage question (increase then decrease or vice versa) has appeared in almost every CGL paper since 2017 — treat it as guaranteed marks
• Successive change and population problems appear at medium difficulty in Tier 1 and harder variants in Tier 2 — nail the formula now
• In DI pie charts and bar graphs, percentage calculation speed depends on knowing fraction-to-percent values by heart — spend 5 minutes daily drilling these
• Time target: direct percentage questions should be solved in under 45 seconds using fraction shortcuts; spending more than 90 seconds means you are doing it the long way