Percentage Questions for AFCAT

What Is Percentage

Percentage simply means 'per hundred'. When you say 40%, you mean 40 out of every 100. It is a universal way to compare quantities on a common scale of 100. Think of it like a cricket batting average — it gives you a standard benchmark regardless of the actual numbers involved.

• Percent symbol % means divided by 100
• To convert fraction to percent: multiply by 100
• To convert percent to fraction: divide by 100
• 25% of 80 means (25/100) x 80 = 20
• Percentage is always calculated with respect to some base value

Percentage Increase and Decrease

This is the most commonly tested percentage concept in AFCAT. You need to find how much a value has gone up or down relative to its original value. Always remember: the base for percentage change is the ORIGINAL value, not the new one. A common trap is using the new value as the base.

• Increase%: new value is more than original
• Decrease%: new value is less than original
• Base is always the original (old) value
• If price increases by 20%, new price = 120% of old price
• If price decreases by 20%, new price = 80% of old price
• Multiplier for r% increase = (1 + r/100); for decrease = (1 - r/100)

Successive Percentage Changes

When two percentage changes are applied one after another, you cannot simply add them. If a value increases by 20% and then decreases by 20%, you do NOT get back to the original. This is a classic AFCAT trap. Use the net effect formula to find the combined result quickly.

• Two successive changes of a% and b% give a net change
• Net change is NOT simply a + b
• If both are increases, net effect is positive but less than a+b
• If one increases and one decreases, net effect depends on values
• Easiest method: apply multipliers one after another on 100

Fraction to Percent Conversion Table

In AFCAT, memorising key fraction-percent equivalents saves 20-30 seconds per question. Instead of calculating, you instantly recall that 1/8 = 12.5%. This is your speed weapon in the exam hall.

• 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%
• 1/5 = 20%, 1/6 = 16.67%, 1/7 = 14.28%
• 1/8 = 12.5%, 1/9 = 11.11%, 1/10 = 10%
• 1/11 = 9.09%, 1/12 = 8.33%, 3/4 = 75%
• 2/3 = 66.67%, 3/8 = 37.5%, 5/8 = 62.5%

Population and Expenditure Type Problems

AFCAT often presents word problems where population, salary, or expenditure changes over years. These are just successive percentage change problems in disguise. Always identify the original value and apply multipliers year by year. You can also use the net effect formula if only two changes are involved.

• Population after 2 years at r% growth = P x (1 + r/100)^2
• These are the same as compound interest problems
• Read carefully whether change is on original or on new value
• Expenditure = Price x Quantity — change in one affects the product
• If price rises by r%, to keep expenditure same, reduce quantity by r/(100+r) x 100%

• Using the new value as the base when calculating percentage change — always use the original value as the base
• Adding two successive percentages directly (e.g. 20% + 20% = 40% net change) — always use the net effect formula
• Confusing 'x% more than y' with 'x% of y' — 20% more than 100 is 120, not 20
• Forgetting the negative sign when one of the successive changes is a decrease in the net formula
• Not converting percentage back to the correct unit in the final answer — e.g. leaving answer as 0.25 instead of 25%

• POBO rule — Percentage Of, Base is Original (always divide by the original/old value for % change)
• Successive changes trick: 20% up then 20% down — imagine blowing a balloon by 20% then letting 20% of the NEW air out. You never get back to start.
• Net formula memory: a + b + ab/100 — remember it as 'add them, then add their product over 100'
• Fraction table shortcut: halve to go from 1/n to 1/(2n) — 1/4=25%, so 1/8=12.5%, 1/16=6.25%

• AFCAT typically has 2-3 percentage questions per paper, often embedded inside profit-loss or data interpretation — brush up these linked topics too
• Questions are mostly moderate: finding percentage change, successive changes, or reverse percentage (finding original from a given percent). Rarely very hard.
• Reverse percentage is a favourite — 'After a 20% increase, value is 600. Find original.' Solve: 600/1.2 = 500. Practice this pattern.
• Time target: pure percentage questions should be solved in under 60 seconds. If it is taking longer, use approximation or fraction-to-percent table.
• Data Interpretation sets in AFCAT often require quick percentage calculations across a table or bar chart — your fraction table memorisation pays off here directly