Percentage Questions for AGNIVEER ARMY

What is Percentage

Percentage means 'out of 100'. When you say 40%, it means 40 out of every 100 parts. Think of it like cutting a roti into 100 equal pieces — 40% means you took 40 pieces. Converting between fractions, decimals, and percentages is the foundation of every percentage question.

• x% = x/100 (always divide by 100 to convert percent to fraction)
• To convert fraction to percent: multiply by 100
• To convert decimal to percent: shift decimal point 2 places right (0.35 = 35%)
• Key fractions to memorize: 1/2=50%, 1/3=33.33%, 1/4=25%, 1/5=20%, 1/8=12.5%, 1/6=16.67%
• A% of B = B% of A (very useful trick to swap values)

Percentage Increase and Decrease

This is the most tested concept. When a value goes up or down, you need to find the percent change compared to the ORIGINAL value (not the new value). Remember: always divide by the original. A common trick in the exam is to give the new value and ask for the original — that is the reverse percentage problem.

• Percent Increase = (Increase / Original) x 100
• Percent Decrease = (Decrease / Original) x 100
• Multiplier for x% increase: (1 + x/100). Example: 20% increase = multiply by 1.2
• Multiplier for x% decrease: (1 - x/100). Example: 15% decrease = multiply by 0.85
• If price increases by x%, to restore original: decrease by x/(100+x) x 100
• If price decreases by x%, to restore original: increase by x/(100-x) x 100

Successive Percentage Change

When two percentage changes happen one after another (like two years of population growth, or two discounts), you cannot simply add them. Use the combined formula. This is a favourite trick question in Agniveer papers — they want you to make the mistake of adding.

• Two successive changes of a% and b% give net change = a + b + (ab/100) percent
• If both are increases, ab is positive. If one is decrease, use negative sign for that value
• Example: 10% increase then 10% decrease is NOT zero — it is -1% (net loss)
• Use multiplier method for speed: just multiply the two multipliers

Percentage in Word Problems (Population, Salary, Marks)

Agniveer papers often wrap percentage inside a story — a town's population grew, a student scored a certain percentage, a worker's salary was cut. The method is the same, only the words change. Read carefully: find out what is the BASE (original 100%) and what is the change or the part being asked about.

• Population after n years = P x (1 + r/100)^n — same as compound interest logic
• Marks problems: Total marks = (Marks obtained / Percentage scored) x 100
• Expenditure = Price x Quantity. If price rises by r%, to keep expenditure same, reduce quantity by r/(100+r) x 100
• If a student passes with x% and needs Y marks to pass, find total marks using Part formula
• Always identify: what is the whole (base) before doing any calculation

• Using the NEW value as base instead of the ORIGINAL value when calculating percent change — always divide by original
• Adding successive percentages directly (e.g., 20% + 10% = 30%) instead of using the formula — this is the classic trap
• Confusing percent increase needed to recover a loss vs the original loss percent — they are different values
• In pass-fail problems, forgetting whether the student failed by X marks or scored X marks above passing — re-read the question
• Mixing up A% of B with B% of A — they are equal in value, but candidates panic and waste time recalculating

• POEM trick for base: P = Part, O = Of (this word tells you the base/whole), E = Equals, M = Multiply by 100. Whenever you see 'of', the number after it is your base.
• Fraction table song — memorize these 8 fractions as a chant: Half-50, Third-33, Quarter-25, Fifth-20, Sixth-17, Eighth-12.5, Ninth-11, Tenth-10. Drill them daily.
• Successive change: think of two tax layers on a shop price. First GST, then discount. You cannot simply add or subtract — the second operates on the already-changed price.
• Multiplier shortcut memory: Increase means 1-POINT-something (1.2 for 20%). Decrease means 0-POINT-something (0.8 for 20%). One is above 1, other is below 1.

• Agniveer Army papers typically give 2 to 3 percentage questions. At least one will be a straightforward 'find X% of Y' type — grab those marks in under 20 seconds using fraction shortcuts.
• One question is usually a word problem mixing percentage with profit-loss or salary. Identify the base first, then apply formula — do not rush into calculation.
• Successive percentage questions appear as tricksters — they look easy but catch students who simply add. If you see two consecutive changes, always use the net formula or multiplier method.
• Pass-fail mark problems are very common in Agniveer. Practice 5-6 of these specifically. The structure is almost identical each time — just the numbers change.
• Time management: pure percentage questions should take 30-45 seconds each. If a question is taking more than 1 minute, skip and return — do not let one question eat into easy marks elsewhere.