Percentage Questions for RRB NTPC

Basic Percentage Concepts

Percent means per hundred. When you say 40%, you mean 40 out of every 100 parts. Converting between percent, fraction, and decimal is the first skill to master. Learn the fraction-to-percent table by heart (1/4 = 25%, 1/3 = 33.33%, 1/8 = 12.5%, etc.) because using fractions instead of long division saves 30-40 seconds per question.

• x% of y = (x/100) x y
• To convert fraction to percent: multiply by 100
• To convert percent to fraction: divide by 100
• Key fractions to memorise: 1/5=20%, 1/6=16.67%, 1/7=14.28%, 1/8=12.5%, 1/9=11.11%, 1/11=9.09%
• If A is x% of B, then B is (100/x)% of A — reverse relationship
• Percentage value = (Part / Whole) x 100

Percentage Increase and Decrease

Percentage change measures how much a value has gone up or down relative to the original value. The original value is always in the denominator. A classic trap: if price increases by 20% and then decreases by 20%, you do NOT get back the original — you lose 4%. This happens because the base changes.

• Percentage Increase = (Increase / Original) x 100
• Percentage Decrease = (Decrease / Original) x 100
• Net change for +a% then -a% = -a squared / 100 percent (always a loss)
• If value increases by x%, new value = Original x (1 + x/100)
• If value decreases by x%, new value = Original x (1 - x/100)
• Always use the OLD value (before change) as the base, never the new value

Reverse Percentage (Finding the Original)

These are tricky questions where the final value is given and you must find the original. The most common mistake is applying the percentage to the final value instead of the original. Think of it this way: if a shirt after 20% discount costs Rs 800, the original price is NOT 800 + 20% of 800. The 20% was on the original, so you work backwards.

• If after x% increase final value is F, then Original = F x 100 / (100+x)
• If after x% decrease final value is F, then Original = F x 100 / (100-x)
• Never apply reverse percentage to the changed value directly
• Shortcut: Use multiplier method — 20% increase means multiplier 1.2, so divide by 1.2 to reverse
• This concept also appears in Profit/Loss (finding Cost Price from Selling Price)

Population and Expenditure Type Problems

These are applied percentage problems common in RRB NTPC. A population grows or declines at a fixed rate each year, or income/expenditure changes and you need to find the net impact. They look complex but simply use the successive change formula or compound multiplier method.

• Population after n years at r% growth = P x (1 + r/100) raised to n
• If price rises by x% and consumption falls by y%, expenditure change = x + (-y) + (x x -y)/100
• If income rises x% but savings fall y%, use actual numbers rather than direct formula to avoid errors
• For 2-year changes, the successive formula works perfectly
• Always identify: what is the base (original) and what is the final value

• Using the new (changed) value as base in percentage change instead of the original value — always divide by the ORIGINAL.
• In reverse percentage, adding x% directly to the final value instead of using the formula Original = Final x 100/(100+x).
• Thinking +20% then -20% cancels out. It does not — you always end up with a net LOSS of (20x20)/100 = 4%.
• Confusing percent of increase with percent more than. If A is 25% more than B, then B is NOT 25% less than A — B is 20% less than A.
• In expenditure problems, applying percentage change to the wrong quantity — always track which percentage applies to price and which to quantity separately.

• POBO Rule: Percentage change = (change/Original) x 100. P-O-B-O means Put Old value at the Bottom — always.
• Successive change formula a+b+ab/100: remember it as ADD then ADD the PRODUCT-by-100. For increase use +, for decrease use minus sign with b.
• Reverse percentage trick: Increase by 20% means x1.2. To reverse, divide by 1.2. Decrease 25% means x0.75. Reverse = divide by 0.75. Think of it as undoing the multiplier.
• Fraction table rhyme: One-fourth is 25, one-fifth is 20, one-eighth is 12.5, one-third is plenty (33.33). Memorise these 8 fractions and convert percentages instantly without long division.

• RRB NTPC frequently gives percentage questions embedded in DI sets — if you know your fraction shortcuts (1/8=12.5%, 3/8=37.5%) you save 20-30 seconds per question in DI.
• Reverse percentage and successive change are the two highest-frequency direct question types in recent RRB NTPC papers — prioritise these over basic percent calculations.
• Expenditure-type questions (price up, consumption down, find net change) appear almost every session — practice the formula Net = a - b - ab/100 with signs carefully.
• Questions in RRB NTPC are mostly 1-step or 2-step — rarely 3-step. If your calculation is going beyond 2 steps, re-read the question; you likely missed a shortcut.
• Time target: Each percentage question should take under 45 seconds. If it is taking longer, use fraction conversion or the multiplier method instead of the full percentage formula.