Percentage - Shortcuts & Tricks for Placement Tests, Job Interviews & Exams

Name: Percentage - Shortcuts & Tricks for Placement Tests, Job Interviews & Exams
Uploaded: 2017-05-15T06:57:45.000Z
Duration: 1 h 42 min 46 s

Understanding Percentages in Quantitative Aptitude

Introduction to Percentages

The tutorial introduces the concept of percentages, emphasizing its importance in quantitative aptitude for placement tests and competitive exams.

The video aims to simplify percentage problems, encouraging viewers to practice on careerite.com, which offers over a thousand aptitude questions.

Definition and Meaning of Percentage

Percentage is defined as "part" of something and is represented by the symbol "%", which means "divide by 100".

An example illustrates that if someone requests 30% of a biscuit, it signifies taking a part from the whole (100%).

Practical Examples of Percentages

A practical scenario involving water in a tank shows that asking for 10% of 80 liters translates mathematically to finding 8 liters.

Understanding percentages is crucial for various applications like discounts and profit/loss calculations.

Common Percentage Values

The video discusses common fractions associated with percentages:

Half = 50%

One-third = approximately 33.33%

One-fourth = 25%

One-fifth = 20%

One-tenth = 10%

Calculating Percentages Easily

Techniques for calculating percentages quickly are introduced; for instance, finding 10% of any number can be simplified by moving the decimal point.

Using an example with the number 260 demonstrates how straightforward it can be to calculate percentages through basic multiplication or decimal adjustments.

Understanding Percentages and Their Calculations

Basic Percentage Calculations

To find 10% of a number, simply move the decimal point one place to the left. For example, 10% of 260 is 26.

To calculate 20%, double the value of 10%. For instance, for 350, first find 10% (35), then multiply by 2 to get 70 as 20%.

Finding percentages can be simplified: for example, to find 1% of a number like 693, move the decimal two places left to get 6.93.

Advanced Percentage Techniques

When calculating percentages close to round numbers (e.g., finding 39% of 260), first calculate a nearby percentage (40%) and adjust accordingly by subtracting the difference.

For example, after finding that 40% of 260 is 104, subtracting the value for 1% (2.6) gives you an easy way to determine that 39% equals approximately 101.4.

Solving Percentage Problems

A quick method for percentages like finding out what percent one quantity is of another involves setting up a fraction: textQuantity_1 / textQuantity_2 times100 .

Example problem: If 56% of y equals 182, rearranging gives y = 182 times100/56, leading to y =325.

Finding Unknown Percentages

To determine what percent one quantity is of another without direct multiplication, set it up as a ratio and multiply by 100.

In this case with quantities like 42 kg out of 336 kg, use the formula: (42/336)times100 =12.5%.

Cross-Multiplication in Percentages

When given relationships between different percentages (like 15% of y equaling 21% of z), cross-multiply to solve for unknown values efficiently.

This method allows you to derive that if you know how much one percentage relates to another, you can easily compute unknown percentages through simple algebraic manipulation.

Price Comparisons Using Percentages

When comparing prices based on percentage differences (e.g., rice being cheaper than wheat), using arbitrary values like $100 simplifies calculations and helps visualize price differences effectively.

Understanding Price Relationships: Rice and Wheat

Calculating the Price of Rice

The price of rice is assumed to be 100 rupees, while wheat is also priced at 100 rupees. Since rice is stated to be 30% less than wheat, the calculation for rice's price involves subtracting 30% of wheat's price from its own.

To find 30% of 100 rupees (the price of wheat), two methods are presented: either directly calculating as 30 div 100 times 100 or recognizing that 10% of 100 is 10, thus multiplying by three gives 30. This results in a final rice price of 70 rupees.

Understanding Percentage Differences

The discussion shifts to determining how much more expensive wheat is compared to rice. It’s emphasized that simply assuming it’s a direct inverse percentage (i.e., if rice is 30% less, then wheat must be 30% more) is incorrect due to differing percentage values.

To calculate this accurately, the formula used involves dividing the price of wheat by the price of rice and multiplying by 100. This yields approximately 142.85%, indicating that wheat costs about 142.85% relative to rice's cost.

Finalizing Percentage Increase

To find out how much more expensive wheat is than rice in terms of percentage, one must subtract the base value (100%) from the calculated value (142.85%), resulting in an increase of 42.85%. Thus, wheat's price exceeds that of rice by this percentage amount.

Price Changes and Their Effects on Consumption

Analyzing Apple Price Changes

A scenario involving apples illustrates how a product's price can change through increases and decreases: starting with an assumed apple price at 100 rupees, which first rises by 10%, leading to a new cost of 110 rupees after adding ten rupees for the increase. Subsequently, a decrease occurs where another ten percent off this new total results in a final apple cost of 99 rupees.

The overall change in apple pricing amounts to a reduction of one rupee from its original cost; when expressed as a percentage relative to its initial value, this equates to a decrease of just 1%. This highlights why percentages are crucial for understanding changes rather than absolute values alone since actual prices may vary widely across different contexts or products.

Sugar Price Increase and Consumption Adjustment

In discussing sugar prices raised by twenty-five percent, it’s noted that maintaining expenditure requires adjusting consumption levels accordingly; initially set at an assumed rate per kilogram (rupee hundred), with consumption pegged at one kilogram leading to an expenditure equal to its rate multiplied by quantity consumed—resulting in an initial expense also being one hundred rupees before any changes occur post-price hike.

After establishing that sugar now costs ₹125 per kg following the increase (with ₹25 added), calculations show that if consumption drops proportionately based on these new rates—specifically down from one kg—to maintain equivalent spending levels would necessitate consuming only around point-eight kilograms instead; hence reducing intake effectively becomes necessary for budget adherence amidst rising costs without altering total expenditures significantly over time.

Understanding Percentage Calculations and Exam Scoring

Percentage Reduction in Consumption

The calculation of percentage reduction is illustrated with an example where a person reduces their consumption by 2 kg. To express this as a percentage, the formula used is (textQuantity 1 / textQuantity 2) times 100. In this case, it results in 0.2 / 1 times 100 = 20%.

Exam Passing Marks Calculation

A student needs to score at least 40% to pass an exam but scores only 20 marks and fails by 40 marks. This leads to the equation for maximum marks M being derived from passing marks: 20 + 40 = (40/100)M. Simplifying gives M = 150.

Analyzing Student Scores

The scenario continues with another student, Y, who scores less than the required passing marks. If Y had scored an additional amount equal to their failing margin (40), they would have passed. This establishes that Y's score was indeed below the passing threshold calculated earlier.

Comparison of Two Students' Scores

A second example involves two students, A and B, where A scores only 10% and fails by 30 marks while B scores significantly higher at 40%. The calculations show how both students relate to the same passing mark through different scoring scenarios leading to a conclusion about maximum possible exam scores being 200.

Understanding Failures in Subjects

In a class scenario, percentages of students failing in science (15%), maths (25%), and both subjects (10%) are discussed. Using Venn diagrams can help visualize these relationships effectively when calculating how many students passed both subjects based on given failure rates. This method simplifies understanding complex overlapping data sets in exams.

Understanding Pass Percentages and Failures in Exams

Calculating Pass Percentage

The pass percentage is calculated by subtracting the failure percentage from 100%. For example, if 40% of students failed, then the pass percentage would be 60%.

This method can lead to incorrect results if there are overlaps in failure categories. In this case, a student who failed both subjects was counted twice.

Identifying Double Counting

When calculating failures, it’s crucial to account for students failing both subjects to avoid double counting. Here, 10% of students were counted in both science (15%) and maths (25%).

After removing the double-counted 10%, the total failure rate adjusted from 40% to 30%, leading to a corrected pass percentage of 70%.

Price Decrease Impact on Rice Purchases

Original Price Calculation

To find the original price of rice per kg after a price decrease, we assume an initial price 'P' and calculate how much rice could be bought with a fixed budget.

Initially assumed that people could buy 8 kg of rice for ₹100; post-decrease, they could buy an additional 10 kg.

Expenditure Consistency

The expenditure remains constant at ₹100 while the amount of rice purchased changes due to price adjustments.

A decrease of 20% in price means that if 'P' is the original price, the new price becomes 0.8P.

Final Price Determination

By setting up equations based on expenditure before and after the price change, we determine that initially people could buy 40 kg of rice for ₹100 at an original rate of ₹2.5 per kg.

Election Vote Analysis

Votes Distribution

In an election with two candidates where one received only 40% of votes but lost by a margin of 1,000 votes.

Total Votes Calculation

Letting 'A' represent total votes cast allows us to express candidate one’s votes as 0.4A, while candidate two receives 0.6A.

Margin Analysis

Since candidate one lost by 1,000 votes, we set up an equation: 0.4A + 1,000 = 0.6A.

Conclusion on Total Votes

Solving gives us that a total of approximately 5,000 votes were cast in this election scenario.

Literacy Rates Among Females

Population Breakdown

Assuming a population size of 100, with 55% being female leads to 55 females and consequently 45 males remaining.

Literacy Rate Calculation

Given that 80% literacy among males translates into literate males being 36.

This structured approach provides clarity on key concepts discussed within each section while maintaining navigability through timestamps linked directly to relevant parts of the transcript.

Understanding Literacy Rates and Percentages

Calculating Male and Female Literacy

The total literacy rate is 58%, meaning out of 100 people, 58 are literate. This indicates a significant portion of the population has basic reading and writing skills.

The male literate population is calculated to be 36. Therefore, the female literate population can be derived as 58 (total literates) - 36 (male literates) = 22 females.

To find the percentage of literate females, we need to express it in relation to the total number of females, which is not provided directly but inferred from context.

Finding Female Literacy Percentage

The formula for calculating the percentage of literate females is: (Number of Literate Females / Total Number of Females) * 100. This ensures that our answer remains consistent with the data presented in percentages.

After calculations, it is determined that 40% of females are literate based on the derived figures.

Solving Percentage Problems

Original Bill Calculation

If a bill has a deduction of 20% and still requires payment of ₹100, this implies that what remains represents 80% of the original bill.

Setting up an equation where 0.8B = ₹100, we solve for B (the original bill), concluding it was ₹125.

Salary Comparisons

A's salary being stated as 50% more than B's leads us to assume B's salary at ₹100; thus A’s salary becomes ₹150.

To determine how much less B's salary is compared to A’s in percentage terms, we calculate: (A - B)/A * 100.

Comparative Analysis Between Two Numbers

Understanding Salary Differences

The difference between salaries shows that B earns ₹50 less than A. Expressing this difference as a percentage yields approximately 33.33%.

Analyzing Two Numbers Relative to a Third

When comparing two numbers both reduced by different percentages from a third number, we set up equations based on their reductions from an assumed value (third number).

Population Changes Due to Events

Impact of Disease on Village Population

Assuming an initial village population M, after losing 10% due to cholera, only 90M/100 remain.

Following this reduction, if another panic causes an additional exodus where remaining inhabitants leave by another percentage (25%), further calculations will reveal how many inhabitants are left post-event.

This structured approach provides clarity on key concepts discussed within the transcript while allowing easy navigation through timestamps for deeper understanding or review.

Understanding Population Percentages in a Village

Calculation of Remaining Population

The remaining population in the village is calculated as 75% of the total, which is derived from the formula: remaining people = (remaining percentage / 100) * total population.

Concept of Percentage Subtraction

The calculation involves subtracting 25% from 100%, not from another percentage like 90%. This is because percentages are always taken relative to a whole, which is considered as 100%.

Application of Given Data

After accounting for the departure of 25%, it was established that only 450 people remained in the village. This figure serves as a critical reference point for further calculations.

Solving for Original Population

The original population was determined through mathematical operations involving multiplication and division. The final calculation revealed that the initial number of inhabitants was 6,000.

Efficiency in Percentage Calculations

With practice, solving percentage-related problems can be done quickly—often within one minute or less. Mastery of these concepts can significantly aid in scoring well on related assessments.