Percentage
About 6 min · Mathematics · English
Time worked out from the lesson's 415 words at 150 words a minute, plus a minute for each question.
Percentage is part of the RRB NTPC Mathematics syllabus. This topic is foundational — profit-loss, simple interest, discount, and even data interpretation questions are built on percentage concepts.
Key ideas
- Definition: Percentage means "out of 100." x% = x/100. It is a ratio or fraction with denominator 100.
- Conversion: Fraction to percentage: multiply by 100. Decimal to percentage: shift decimal point two places right. Percentage to fraction: divide by 100 and simplify.
- Percentage of a quantity: x% of N = (x/100) × N. To find "what percent A is of B," calculate (A/B) × 100.
- Percentage change formula: Percentage change = [(New Value − Old Value) / Old Value] × 100. Positive result = increase, negative = decrease.
- Successive changes: Two successive changes of a% and b% do not simply add. Net effect = a + b + (ab/100). Sign matters: increase is +, decrease is −.
Watch out for
- Adding successive percentages directly: Students often add 20% increase and 10% decrease to get 10% net increase. Fix: Use the formula a + b + (ab/100). The compounding effect changes the result.
- Using wrong base for percentage change: Computing percentage increase/decrease using the new value instead of the original. Fix: Always divide the change by the original value, not the new one.
- Confusing "x% of y" with "y% of x": While mathematically x% of y = y% of x, in word problems context matters. Read carefully which quantity is the base. Fix: Identify the base (the quantity after "of") clearly.
Quick reference
- x% = x/100. To find x% of N: (x × N)/100.
- Percentage change = [(New − Old)/Old] × 100.
- Successive changes of a% and b%: Net = a + b + ab/100.
- If A is x% more than B, then B is [x/(100+x)] × 100% less than A.
- Reverse calculation: If x% of N = R, then N = (R × 100)/x.
Check yourself: 3 questions
1. A student scored 432 marks out of 600 in an examination. What percentage of marks did the student score?
2. The population of a town is 50,000. If the population increases by 10% in the first year and then decreases by 10% in the second year, what is the population at the end of two years?
3. In an election between two candidates, one candidate got 55% of the total valid votes. If 20% of the votes were declared invalid and the total number of votes was 7,500, find the number of valid votes the other candidate got.
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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