Percentage

About 6 min · Mathematics · English

Time worked out from the lesson's 380 words at 150 words a minute, plus a minute for each question.

Percentage is a topic in the Mathematics section of Maharashtra Police Bharti exam. The word "percent" means "per hundred" — so 25% simply means 25 out of 100. This concept forms the foundation for many other topics like Profit & Loss, Simple & Compound Interest, and Data Interpretation.

Key ideas

Basic Definition: x% = x/100. To find x% of a number N, calculate (x × N)/100.
Percentage to Fraction: Divide by 100 and simplify. Example: 25% = 25/100 = 1/4.
Fraction to Percentage: Multiply by 100. Example: 3/5 = (3/5) × 100 = 60%.
Percentage Increase/Decrease: When a value changes from A to B, the percentage change = [(B − A)/A] × 100. Positive result means increase, negative means decrease.
Successive Percentage Change: When two successive changes of a% and b% occur, the net effect = a + b + (ab/100)%. This is crucial for discount-on-discount and population growth problems.

Watch out for

Wrong base in comparison: "A is 25% more than B" — students calculate 25% of A instead of B. Fix: The base is always what comes after "than" or "of".
Adding successive percentages directly: Two successive 10% increases ≠ 20% increase. Fix: Use the formula a + b + (ab/100). Two 10% increases = 10 + 10 + 1 = 21%.
Confusing increase and decrease reversal: If something increases by 20%, it does NOT decrease by 20% to return to original. Fix: A 20% increase needs a 16.67% decrease (1/6) to reverse.

Quick reference

x% of N = (x × N)/100 — the most basic formula.
Percentage change = (Difference/Original) × 100 — always divide by the OLD value.
Successive changes of a% and b% = a + b + (ab/100)% — negative sign for decrease.
To reverse x% increase, decrease by (100x)/(100 + x)%.
25% = 1/4, 20% = 1/5, 12.5% = 1/8 — memorize these for speed.

Check yourself: 3 questions

1. A candidate scored 432 marks out of 600. What is his percentage?
2. The population of a town is 45000. If it increases by 8% in the first year and 12% in the second year, what will be the population after 2 years?
3. A shopkeeper marks his goods 40% above the cost price and gives a discount of 15%. What is his profit percentage?

This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 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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