UP Police Constable · Bite-size lessons
Percentage
About 7 min · Numerical & Mental Ability · English
Time worked out from the lesson's 460 words at 150 words a minute, plus a minute for each question.
Percentage is a topic in the Numerical & Mental Ability section of UP Police Constable exam. The word "percent" means "per hundred" — so 25% literally means 25 out of every 100. This concept appears both as direct calculation questions (convert fractions to percentages, find x% of y) and in applied word problems involving marks, population, consumption, elections, and price changes.
Key ideas
- Definition: Percentage expresses a number as a fraction of 100. If a quantity is x out of y, then percentage = (x/y) × 100%.
- Conversion clarity: To convert percentage to fraction, divide by 100. To convert fraction to percentage, multiply by 100. For example, 3/4 = (3/4) × 100 = 75%.
- Percentage increase/decrease: If a value changes from A to B, percentage change = [(B - A)/A] × 100%. Positive result means increase, negative means decrease.
- Successive percentage changes: When two percentage changes apply consecutively, the net effect is NOT their simple sum. Use the formula: Net% = a + b + (ab/100), where a and b are the two percentage changes.
- Percentage of a percentage: "x% of y%" means (x/100) × (y/100) × original value. This is common in population or consumption problems.
Watch out for
- Confusing base for percentage change: Students calculate percentage of new value instead of original. Fix: Percentage change is always with respect to the ORIGINAL value unless stated otherwise.
- Adding successive percentages directly: Thinking 10% increase followed by 20% increase = 30% increase. Fix: Use the formula a + b + (ab/100). The correct answer is 32%, not 30%.
- Reversing percentage incorrectly: Believing that a 25% increase can be reversed by 25% decrease. Fix: If increased by 25%, to reverse, decrease by [25/125 × 100] = 20%.
Quick reference
- 50% = 1/2, 33.33% = 1/3, 25% = 1/4, 20% = 1/5, 12.5% = 1/8 — memorize these for instant conversion.
- Successive changes formula: Net% = a + b + ab/100 (divide product by 100).
- Percentage increase: New = Old × (1 + r/100); Percentage decrease: New = Old × (1 - r/100).
- To find original after x% increase: Original = New/(1 + x/100).
- Passing marks: Max = (Scored + Shortfall) × 100/Pass%.
Check yourself: 3 questions
1. A fruit seller had 600 apples. He sold 35% of them in the morning and 40% of the remaining in the evening. How many apples does he have left?
2. The population of a town is 50,000. If it increases by 10% in the first year and decreases by 20% in the second year, what will be the population at the end of two years?
3. A student scores 432 marks out of 600. In order to pass, a minimum of 33% marks is required. By what percentage does the student's score exceed the passing marks?
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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