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Percentage - Shortcuts & Tricks for Placement Tests, Job Interviews & Exams
CareerRide
Overview
This video tutorial explains the fundamental concept of percentages and provides practical shortcuts and tricks for solving problems commonly found in placement tests, job interviews, and competitive exams. It breaks down the meaning of percentage as a 'part' and 'divide by 100,' illustrates common percentage-to-fraction conversions, and demonstrates quick calculation methods for percentages like 10% and 1%. The video then walks through various word problems, including those involving price changes, consumption, election votes, and population demographics, offering step-by-step solutions and emphasizing efficient problem-solving strategies.
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Chapters
- Percentage fundamentally means a 'part' of a whole.
- The '%' symbol signifies 'divide by 100'.
- An entire whole is always considered 100%.
A clear grasp of these core definitions is essential for accurately interpreting and solving any percentage-related problem.
10% of 80 liters of water means (10/100) * 80 liters, which equals 8 liters.
- Familiar fractions have direct percentage equivalents (e.g., 1/2 = 50%, 1/4 = 25%).
- Understanding these conversions simplifies calculations.
- Key equivalents include 1/3 ≈ 33.33%, 1/4 = 25%, 1/5 = 20%, 3/4 = 75%, 1/8 = 12.5%.
Memorizing these common conversions allows for faster problem-solving by bypassing lengthy calculations.
If someone wants 1/4 of an object, they want 25% of it.
- To find 10% of a number, simply move the decimal point one place to the left.
- To find 1% of a number, move the decimal point two places to the left.
- Larger percentages can be calculated by combining known percentages (e.g., 40% = 4 * 10%, 39% = 40% - 1%).
These shortcuts significantly reduce the time needed to calculate percentages, crucial for timed exams.
10% of 260 is 26.0 (by moving the decimal one place left); 1% of 260 is 2.60 (by moving the decimal two places left).
- Problems asking 'what percent is A of B' require the formula (A / B) * 100.
- When finding a percentage of an unknown ('X% of Y is Z'), set up the equation (X/100) * Y = Z.
- Problems involving 'less than' or 'more than' require careful identification of the base value for percentage calculation.
These examples demonstrate how to translate common percentage scenarios into mathematical equations for accurate solutions.
To find what percent 42 kg is of 336 kg, calculate (42 / 336) * 100 = 12.5%.
- When comparing two values where one is a percentage more or less than the other, use the difference relative to the second value.
- Successive percentage changes (increase then decrease, or vice versa) do not simply cancel out.
- For problems where an arbitrary value (like price or population) is unknown, assume 100 for easier calculation.
This section addresses common pitfalls in percentage problems, such as assuming symmetrical changes or misidentifying the base for comparison.
If a price increases by 10% and then decreases by 10%, the final price is 99% of the original, not 100%.
- To maintain constant expenditure with a price increase, consumption must decrease by a specific percentage.
- In elections, the difference in votes between candidates is directly related to the percentage difference in votes cast.
- Demographic problems often require calculating percentages of subgroups and then finding percentages within those subgroups.
These examples show the practical application of percentages in everyday situations like budgeting, voting, and understanding population statistics.
If the price of sugar increases by 25%, consumption must decrease by 20% to keep expenditure the same.
- Passing marks can be determined by relating scores, failure margins, and percentage requirements.
- Problems involving overlapping sets (e.g., students failing multiple subjects) require careful use of the principle of inclusion-exclusion to avoid double-counting.
- The formula for the union of two sets is |A U B| = |A| + |B| - |A ∩ B|, applied here to failing students.
These complex scenarios test the ability to combine multiple percentage concepts and logical reasoning to find a solution.
If 15% fail Science, 25% fail Maths, and 10% fail both, then 30% failed at least one subject (15 + 25 - 10).
- Calculating original values when a percentage discount or increase has been applied is a common problem type.
- Understanding how price changes affect consumption while keeping expenditure constant is key to personal finance.
- Percentage differences are crucial for comparing salaries, prices, and economic indicators.
These applications highlight how percentages are fundamental to financial literacy, from personal budgeting to understanding economic policies.
If 20% of an electricity bill is deducted and Rs. 100 remains, the original bill was Rs. 125.
Key takeaways
- Percentage is a versatile tool representing parts of a whole and is calculated by dividing by 100.
- Mastering common fraction-to-percentage conversions significantly speeds up problem-solving.
- Quick calculation tricks for 10% and 1% are invaluable for rapid estimations and exact calculations.
- Word problems require careful identification of the base value and the relationship between quantities.
- Successive percentage changes do not cancel each other out; the base changes with each step.
- Assume 100 as a base value when dealing with unknown quantities in percentage problems.
- Problems involving overlapping categories require accounting for double-counting using the inclusion-exclusion principle.
Key terms
PercentagePartWholeFractionDecimal PointBase ValueExpenditureConsumptionLiteracy RateInclusion-Exclusion Principle
Test your understanding
- What are the two core meanings of the term 'percentage'?
- How can you quickly calculate 10% and 1% of any given number?
- Explain the strategy for solving problems where a price increases, but you want to maintain the same expenditure.
- How do you approach problems involving overlapping sets, such as students failing multiple subjects?
- Why is it important to identify the 'base value' when calculating percentage increases or decreases?