Percentage literally means "per hundred" — it is a ratio where the denominator is always 100. When you say "30% of passengers carry luggage," you mean 30 out of every 100 passengers carry luggage. That is all percentage ever is: a fraction with 100 in the denominator, expressed with the % symbol.
Here is the analogy that makes this click permanently. Imagine a train with exactly 100 seats. Whatever fraction of seats are occupied, that fraction's numerator is the percentage. 75 seats occupied = 75%. This mental model handles every percentage question — increase, decrease, comparison — because you are always rescaling to a base of 100.
Three things every percentage question asks you to find, in some form:
The formula connecting all three:
Rearranged:
That third rearrangement is the one most students forget, and it is the one RRB Group D loves to test. "There were 280 accidents this year, which is 70% of last year — find last year." That is Base = Part × (100/Percentage).
Percentage questions in RRB Group D fall into four buckets: finding the base from a reduced/increased value, successive percentage change, set overlap (two conditions, find both), and direct fraction-to-percent conversion. Learn to spot which bucket a question falls into, and you have already done half the work.
Stop computing these in the exam hall. These are fixed values — burn them in.
| Fraction | Percentage | |---|---| | 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% | | 3/4 | 75% | | 2/3 | 66.67% | | 3/5 | 60% |
The reverse table matters just as much: 20% = 1/5, 25% = 1/4, and so on. When a question says "decreased by 20%," the new value is 4/5 of the original. Work in fractions when they are clean — it is faster than working in decimals.
This is the most tested form. Pattern: "After a change of X%, the result is Y — find the original."
Use + if the value increased to reach Y, use − if it decreased to reach Y.
Example: Accidents decreased by 30%, result is 280.
When two percentage changes happen one after the other (like two years of growth), do NOT add them. They compound.
where a and b are the two percentage changes (use negative sign for decreases).
Example: +15% then −10%:
This formula saves you from starting with a base of 100 and computing step by step — though that method also works if you prefer it.
Revenue = Price × Passengers. If Price changes by p% and Passengers change by q%, the net revenue change is:
Same formula as successive change. Example: Price +25%, Passengers −20%:
Zero change. That is the answer to one of the PYQs below.
When you are told what percentage passed/failed in two subjects:
"Pass% in at least one" = 100% − "Fail% in both."
So the working formula is:
Example: 72% passed Math, 68% passed GK, 15% failed both.
This is the inclusion-exclusion principle applied to percentages. The formula looks different from what you see in textbooks, but the logic is the same: total = A + B − (A and B).
Some RRB Group D questions link percentage to work. If helper's efficiency is 80% of maintainer's, then helper does 0.8 units of work per day compared to maintainer's 1 unit per day. Since Time = Work/Rate:
Note: Higher efficiency → less time. So if efficiency is 80% (less than 100%), the helper takes more time, not less.
Instead of computing "increase by 25%" as adding 25% of the value, multiply directly by 1.25. For a decrease of 16%, multiply by 0.84. Chain two changes by multiplying two factors.
Example: +25% then −16% on base 100: 100 × 1.25 × 0.84 = 100 × 1.05 = 105 → 5% increase.
Standard method: compute 25% of 100 = 25, add to get 125, then compute 16% of 125 = 20, subtract to get 105. That is 5 steps. Multiplier method: one multiplication line. Time saved: ~20 seconds per question.
For any two successive percentage changes a% and b%, net change = a + b + ab/100. Use negative values for decreases.
Example: +15% and −10% → 15 − 10 + (15)(−10)/100 = 5 − 1.5 = 3.5% net increase.
Standard method: assume base 100, apply first change, then second change, compute difference. That is 4 arithmetic steps. This formula: 3 arithmetic operations. When a and b are both multiples of 5, ab/100 is always a whole or half number — zero mental load.
When a value decreases by X% to reach Y, the original = Y × (100/(100−X)). When X is 20%, 25%, or 30%, convert to fractions immediately.
Example: decreased by 30% → 280. Original = 280 × 10/7 = 400.
Standard method: set up equation 0.7x = 280, solve x = 280/0.7 = 400 (involves decimal division). Fraction method: 280 × 10/7 = 40 × 10 = 400 in two mental steps. Saves ~15 seconds.
For two-subject pass/fail overlap questions, one line does it all: Both = Pass_A + Pass_B − (100 − Fail_both).
Mentally: add the two pass percentages, subtract the "passed at least one" number.
Example: 72 + 68 = 140. Passed at least one = 85. Both = 140 − 85 = 55.
Standard method: draw a Venn diagram, label regions, set up equations. That is 4−5 steps. This formula: 3 additions/subtractions. Saves 30−40 seconds in exam conditions.
If efficiency is given as a percentage of another worker's efficiency, flip it to get the time ratio. Efficiency 80% → Time ratio = 100/80 = 5/4.
So if the reference worker takes 15 days: helper takes 15 × 5/4 = 75/4 = 18.75 days.
Standard method: compute per-day work for each, set up equation, solve. Three separate steps. Substitution: one fraction multiplication. Note the direction — lower efficiency always means more days, so if your answer is less than the reference time, you have the fraction inverted.
Read the question once and classify it into one of these four types:
Type 1 — Find the Base: Keywords: "after a change of X%, the value became Y." Use Original = Y × (100 / (100 ± X)). Determine sign: increased to reach Y → use +, decreased to reach Y → use −.
Type 2 — Successive Change: Two percentage changes applied one after another. Use net% = a + b + ab/100. If it is a product (revenue = price × quantity), same formula applies.
Type 3 — Set Overlap: Two conditions (passed in A, passed in B, failed in both). Use Both = A + B − (100 − Fail_both).
Type 4 — Direct Calculation: "X% of Y" or "what % is X of Y." Plug into Part = (P/100) × Base or P% = (Part/Base) × 100.
Decision rule: if the question mentions "original" or "last year" and gives you the current value → Type 1. If two changes happen sequentially → Type 2. If there are two groups with overlap → Type 3. Everything else → Type 4.
Do not start calculations before classifying. That classification step takes five seconds and prevents the most common errors.
Why this question: The classic reverse-percentage trap — students calculate 30% of 280 and subtract instead of finding the base.
Solving path: Decreased by 30% means current value = 70% of original. So original = 280 ÷ 0.70. Faster with fractions: 280 × (10/7) = 400. Check: 30% of 400 = 120, and 400 − 120 = 280. Confirmed.
Why this question: Revenue = Price × Quantity is tested in disguise. Many students see +25% and −20% and guess "5% increase" by adding the two.
Solving path: Apply the product change formula: 25 + (−20) + (25)(−20)/100 = 5 − 5 = 0%. Net change is zero. Alternatively, 100 × 100 = 10,000 original revenue; 125 × 80 = 10,000 new revenue. Same result, zero change.
Why this question: Set overlap is tested with railway-exam framing. The Venn diagram approach wastes 60+ seconds.
Solving path: Failed in both = 15%, so passed in at least one = 85%. Both = 72 + 68 − 85 = 140 − 85 = 55%.
Why this question: Two-year successive change — the classic mistake is 25 − 16 = 9% increase.
Solving path: Net% = 25 + (−16) + (25)(−16)/100 = 9 − 4 = 5% increase. Or: 100 → 125 → 125 × 0.84 = 105. Net = 5% increase.
Why this question: Salary successive change with mixed signs. Direct application of the ab/100 formula.
Solving path: Net% = 15 + (−10) + (15)(−10)/100 = 5 − 1.5 = 3.5% increase.
Why this question: Direct percentage of total — tests whether you remember that percentages must add to 100.
Solving path: Children% = 100 − 36 − 44 = 20%. Number of children = 20% of 1500 = 0.20 × 1500 = 300.
Why this question: Efficiency-time inverse relationship — lower efficiency means more time, not less.
Solving path: Helper does 80% of maintainer's work per day. Time = Work / Rate. Helper's time = Maintainer's time / 0.80 = 15 / 0.80 = 15 × (5/4) = 18.75 days. Sanity check: helper is slower, so 18.75 > 15. Correct direction.
Why this question: Reverse percentage on a percentage itself — "improved by 40%, result is 84%."
Solving path: Let original efficiency = x. After 40% improvement: 1.4x = 84. So x = 84 / 1.4 = 60%. In fractions: 84 × (10/14) = 84 × (5/7) = 60.
Adding successive percentages directly. +25% then −16% is not +9%. The second change applies to the already-changed value, not the original. Always use the multiplier method or the ab/100 formula.
Reversing the direction in efficiency-time problems. If efficiency is 80% of another's, time is (100/80) = 5/4 times more, not (80/100) = 4/5 times less. Lower efficiency always means higher time.
Using 280 as the base in reverse percentage. In "decreased by 30% to give 280," the 280 is the part, not the base. The base (last year's value) is what you need to find. The formula is always Base = Part × (100 / percentage of base that the part represents).
Ignoring the sign of ab in the net change formula. When one change is positive and one is negative, the ab term is negative, which reduces the net change. Students who forget the sign get 3.5% = 5% (net salary question) — a full mark dropped.
In set overlap, forgetting to convert "fail both" to "pass at least one." The formula requires "passed at least one," not "failed both." One subtraction step: pass-at-least-one = 100 − fail-both. Skip this step and your answer is off by the fail-both percentage.
Confusing "X% more than Y" with "X% of Y." "20% more than 80" = 80 + 16 = 96, not 20% of 80 = 16. The phrase "more than" means you add to the base, not just compute the fraction.