Percentage — RRB NTPC Mathematics
This topic carries roughly 10% of Mathematics's 30 questions — tied for the single heaviest topic in the section — and its logic underpins Profit & Loss and Interest calculations elsewhere in the paper. Get the base right, and the rest is straightforward arithmetic.
1. What RRB NTPC actually asks
Expect direct percentage-of-a-number calculations, percentage change (increase/decrease) problems, successive percentage change, "what percent is X of Y" reverse problems, and word problems (elections, salary changes, population growth) built around these core operations.
2. The core percentage formulas
Percentage of a number: (percentage/100) × number.
Percentage change: ((new value − old value) / old value) × 100.
What percent is X of Y: (X/Y) × 100.
3. Successive percentage change
For two successive percentage changes a% and b% (signed — negative for a decrease), the net change is a + b + (ab/100) percent. A 20% increase followed by a 20% decrease is NOT 0% net change — it's a + b + ab/100 = 20 − 20 + (20×−20)/100 = −4%, a net decrease.
4. Finding the original value
If a value has changed by a known percentage to reach a known result, work backward: if a number decreased by 25% equals 90, the original number = 90 / (1 − 0.25) = 90 / 0.75 = 120.
Worked examples
Q1. A number is increased by 20% and then decreased by 20%. What is the net percentage change?
Pick an option to check your answer.
Show explanation
Solution. Using the successive-change formula with a = 20, b = −20: net change = 20 + (−20) + (20×−20)/100 = 0 − 4 = −4%.
Verify directly: start at 100, increase 20% to 120, decrease 20% of 120 (24) to 96 — a net decrease of 4, not back to 100. Answer: (c).
Q2. In an election with two candidates, the winner received 60% of the total votes and won by 4,800 votes. What was the total number of votes cast?
Pick an option to check your answer.
Show explanation
Solution. If the winner got 60%, the loser got 40%. The margin is 60% − 40% = 20% of the total votes, and this equals 4,800. So total votes = 4,800 / 0.20 = 24,000.
Verify: 60% of 24,000 = 14,400 (winner); 40% of 24,000 = 9,600 (loser); margin = 14,400 − 9,600 = 4,800, matching exactly. Answer: (c).
6. Common traps
- Applying successive percentage changes by simple addition. A 20% rise then a 20% fall is a net −4%, not 0% — always use the a+b+ab/100 formula.
- Losing track of the correct base at each step. In multi-step problems, always identify what 100% refers to before each calculation — a discount on a marked-up price is calculated on the marked price, not the original cost.
- Confusing "what percent of" direction. "What percent is 45 of 180" is (45/180)×100, not (180/45)×100 — the second number in "X of Y" phrasing is always the base.
- Working forward instead of backward for "find the original value" problems. If a value results from a percentage decrease, divide by (1 − rate), don't multiply.
7. Guessing strategy
For percentage-change word problems, a rough sanity check (should the answer be larger or smaller than a natural reference point?) usually eliminates at least one clearly wrong-direction option, clearing the guessing threshold.
Summary
- Percentage is roughly 10% of Mathematics's 30 CBT 1 questions — tied for the section's heaviest single topic.
- Percentage of a number: (percentage/100) × number. Percentage change: (new−old)/old × 100.
- Successive percentage change uses a + b + (ab/100), never simple addition.
- To find an original value from a percentage decrease result, divide by (1 − rate); for an increase result, divide by (1 + rate).
- Always track which value is the base ("100%") at each step of a multi-step problem.
- "What percent is X of Y" is always (X/Y) × 100 — Y is the base.
