Percentage Questions for SSC GD

What is Percentage

Percentage means 'per hundred'. If you score 45 out of 50, your percentage is (45/50) x 100 = 90%. Think of it as a common language to compare different quantities on a scale of 100. The symbol % simply means divide by 100.

• x% of y = (x/100) x y
• To convert fraction to percent: multiply by 100
• To convert percent to fraction: divide by 100
• 25% = 1/4, 50% = 1/2, 75% = 3/4, 20% = 1/5, 33.33% = 1/3
• Memorise fraction-percent pairs to save calculation time in exam

Percentage Increase and Decrease

When a value goes up or down, we express the change as a percentage of the ORIGINAL value. This is a very common trap — always divide by the original, not the new value. If price goes from 200 to 250, increase = 50, original = 200, so % increase = (50/200) x 100 = 25%.

• % Increase = (Increase / Original) x 100
• % Decrease = (Decrease / Original) x 100
• If a value increases by R%, new value = Original x (1 + R/100)
• If a value decreases by R%, new value = Original x (1 - R/100)
• Always use ORIGINAL value in the denominator

Finding Original Value (Reverse Percentage)

SSC GD frequently asks: 'After a 20% increase, the price is 600. What was the original price?' Here you work backwards. If 120% of Original = 600, then Original = 600 x 100/120 = 500. Many students wrongly subtract 20% from 600 — that is the biggest mistake in this topic.

• If value after R% increase = X, then Original = X x 100 / (100 + R)
• If value after R% decrease = X, then Original = X x 100 / (100 - R)
• Never apply the percentage directly to the new value to reverse
• Think of it as: New value IS a percentage of original — solve accordingly

Successive Percentage Change

When two percentage changes happen one after another (like two discounts, or population growing for two years), you cannot simply add them. A 10% increase followed by 10% decrease does NOT give you 0% change. Use the combined formula to get the net effect in one step.

• Two successive changes of a% and b% give net change = a + b + (ab/100) percent
• If both are increases, use positive values
• If one is decrease, use negative value for that one
• 10% up then 10% down = 10 + (-10) + (10 x -10)/100 = 0 - 1 = -1% net (a loss of 1%)
• This is also used in population problems over multiple years

Income, Expenditure and Savings Problems

A common SSC GD question type: 'If income increases by 20% and expenditure increases by 10%, what is the percentage change in savings?' Here Savings = Income - Expenditure. Assign easy numbers (like Income = 100, Expenditure = 60, Savings = 40), apply the changes, and find new savings. Then calculate % change in savings.

• Assume convenient values — Income = 100 is always a smart starting point
• Calculate new income, new expenditure, find new savings
• % change in savings = (Change in Savings / Old Savings) x 100
• This method works for marks, population and any part-whole problem

• Applying reverse percentage wrongly — if price rises 20% to reach 600, students subtract 20% of 600 instead of using 600 x 100/120. Always reverse with the formula.
• In percentage change, dividing by new value instead of original value. Change is always over the ORIGINAL.
• Adding successive percentages directly — 10% + 10% is NOT 20% net. Always use the successive change formula.
• Confusing 'what percent of A is B' with 'what percent of B is A' — read the question twice, the order matters completely.
• Not converting fractions to percentages quickly — students waste time calculating instead of using memory shortcuts like 1/8 = 12.5%, 1/6 = 16.67%.

• ORIGINAL is the KING — all percentage change calculations divide by the original value, never the new one.
• Fraction-Percent cheatsheet to memorise: 1/2=50, 1/3=33.33, 1/4=25, 1/5=20, 1/6=16.67, 1/8=12.5, 1/10=10, 3/4=75.
• Successive change trick: think of it as an extra penalty — two 10% changes give you a 1% extra penalty (the ab/100 term always reduces the total).
• For reverse problems say to yourself: The NEW number is a PERCENT of ORIGINAL — set up the equation that way and you will never go wrong.

• SSC GD Maths has 25 questions in 30-35 minutes. Percentage appears 2-3 times. These are medium difficulty and should be solved in under 60 seconds each using fraction shortcuts.
• Most common question types in recent SSC GD papers: reverse percentage (find original price), income-savings problems, and population growth using successive change.
• Use the assumption method (take Income = 100 or Population = 1000) to avoid fraction-heavy calculations. This alone can save 30-40 seconds per question.
• Do not pick answer choices by elimination in percentage questions — small errors compound fast. Always verify with the formula.
• If you see the word 'successive' or 'consecutive' or 'two years' in a question, immediately think of the net change formula a + b + ab/100. It is almost always needed.