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Questions and Answers
What is the symbol used to represent percentages?
If 25% of a number is 80, what is the number?
What happens to a population if it decreases by 30% from its original value?
How would you find an increase of 15% in a quantity?
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What does it mean when we say '50% of X is Y'?
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If a population increases by 20%, what would happen to a town with 5000 residents?
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When scaling quantities according to percentages, what is crucial to understand?
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If a salary is to be increased by 20%, what should be multiplied by to calculate the new salary correctly?
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What is a common mistake to avoid when increasing a salary by a percentage?
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How can aspiring candidates confidently tackle arithmetic-based questions on BPSC examinations?
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What should candidates strive to do while interpreting given information for percentage problems?
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Why is it important to practice solving proportionally similar problems related to percentages?
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Study Notes
Percentage Essentials for BPSC Exam Preparation
Percentages may seem simple at first glance, but they're an essential tool when it comes to tackling questions in various competitive exams like the Bihar Public Service Commission (BPSC) exams. Confidence with percentages can elevate your problem-solving abilities by allowing you to approach complex situations more easily. Let's delve into some of the fundamental concepts related to percentages that will bolster your preparations.
Definition and Basics
A percentage is a fractional value expressed using the symbol "%," where the numerator represents a portion of the denominator. For example, if we say that x% of y equals z, this translates to (x/100)*y = z. Common basic operations involving percentages include finding:
- A percentage of a quantity (multiplying a number by a decimal equivalent of a percentage)
- An increase or decrease in a quantity represented as a percentage
- Finding the original amount based on its increased/decreased version presented as a percentage
Here are three examples illustrating these operations:
- If 80% of 100 is X, then X = (80/100)*100 = 80.
- If the population decreases by 10%, what would happen to a city with 1 million residents? This means the new population would be (10^6 - (10% \times 10^6) = 900,000).
- If the cost of an item increases from Rs. 500 to Rs. 600 due to taxes, find out how much tax was added, which amounts to (600 - 500 = 100 = (\text{tax rate} / 100)\times 500 = 0.1\times 500 = 50). Therefore, 10% tax was added.
Scaling up or down
When scaling quantities according to percentages, it's crucial to understand whether the percentage refers to adding something onto an existing total or reducing the initial figure. Be careful while dealing with such scenarios, since confusion regarding addition versus multiplication could result in incorrect answers.
For instance, let's consider a situation requiring us to raise someone's salary by 20%. In order to determine the exact growth in their income, remember that multiply the current wage by 1 + (percentage/100), rather than simply adding the percentage to the base figure. So, increasing a salary by $60K to $72K ($60K * (1+0.2)) makes sense, whereas doubling the wage to $120k doesn't fit here.
Important tips for practicing percentage problems
- Be vigilant while interpreting the given information - make sure you have correctly understood whether you need to calculate a percentage or solve an inverse percentage problem.
- Strive to grasp the underlying concept instead of relying completely on formulas – try to think logically; convert percentages into decimals wherever possible.
- Practice solving proportionally similar problems, especially those concerning discounts, profit margins, interest rates, etc., which frequently appear on examinations.
By mastering the intricacies and nuances associated with percentages, aspiring candidates can confidently tackle challenging arithmetic-based questions often found in the BPSC examinations. Remember, building proficiency through consistent practice will enable you to apply these principles effortlessly during the examination itself.
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Description
Enhance your problem-solving abilities for Bihar Public Service Commission (BPSC) exams by mastering fundamental concepts related to percentages. Learn how to calculate percentages of quantities, determine increases or decreases, and scale quantities up or down accurately. Gain important tips for practicing percentage-related problems for competitive exams.
