Percentage Calculation Introduction

Introduction to Percentage Calculations

• The session focuses on understanding percentage concepts, shortcuts, and applications in data interpretation and arithmetic topics like simple and compound interest, profit and loss, and mixtures.

Importance of Calculation Skills in Percentage

• Many students struggle with percentage calculations due to making errors or taking too much time.
• Despite the availability of calculators in exams like CAT, relying on them for every calculation is inefficient and not allowed in exams like IPMAT Rohtak and JIPMAT.

Basic Percentage Calculations

• Finding 50% of a number involves halving it (e.g., 50% of 480 is 240).
• Finding 10% of a number involves placing a decimal point (e.g., 10% of 480 is 48).
• Finding 5% of a number can be done by finding 10% and halving it.
• Finding 1% of a number involves placing a decimal point (e.g., 1% of 480 is 4.80).
• Finding 0.5% involves halving 1% of the number.

Breakdown of Complex Percentage calculations

• To find 61% of a number, break it down into 50% + 10% + 1%.
• For example, 61% of 480 can be calculated as (50% of 480) + (10% of 480) + (1% of 480) = 240 + 48 + 4.80 = 292.8.
• Similarly, finding 18.5% of a number requires efficient calculation techniques.

Key Arithmetic Topics

• Mastering percentages, ratios, averages, numbers, HCF, LCM, and divisibility rules is crucial for solving 60-70% of CAT problems.

Percentages and Problem Solving

• One can potentially score well on exams, including CAT and others, by focusing on proficiency in numbers, percentages, ratios, and averages.
• Mastering these four topics alone could cover 60-70% of what is needed to pass some exams.

Calculation Techniques

• To calculate 88.5% of 480, one can subtract 20%, 1%, and 0.5% from the whole.
• 20% of 480 is 96.
• 1% of 480 is 4.8.
• 0.5% of 480 is 2.4.
• Therefore, 88.5% of 480 can be found by 96 - 4.8 - 2.4, which is 88.8

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Percentage Calculation Shortcuts

• 37.5% equals 3/8.
• If asked to find 37.5% of 720, one should calculate 3/8 of 720.
• 3/8 of 720 is 270.
• 33.33% is equivalent to 1/3.
• 33.33% of 720 is 240.
• 16.66% is equivalent to 1/6.
• 83.33% is 100% - 16.66%, making it 5/6.
• Therefore, 83.33% of 720 becomes 5/6 of 720.
• 5/6 of 720 is 600.

Notifications

• CMAT notification is expected around January 28th or 29th.
• The CMAT exam is most likely going to be around March 23rd or 24th

Simple and Compound Interest Problems

• To calculate the simple interest after 4.5 years at 6% per annum on ₹55000, find 27% of ₹55000.
• Simplify the calculation by finding 30% (₹16500) and subtracting 3% (₹1650).
• The simple interest calculates to ₹14850.

Profit Percentage Problems

• Method to find the profit made if a shopkeeper makes a profit of 62.5% selling an article The article's cost price is ₹1280.
• 62.5% is equivalent to 5/8.
• Calculate 5/8 of 1280
• 5/8 of 1280 is ₹800.

Mixture Percentage Problems

• 710 ml of milk, 350 ml of vanilla syrup, and 170 ml of sugar syrup are combined.
• Find the percentage of sugar syrup in the final mixture.
• The total mixture volume is 710 + 350 + 170 = 1230 ml.
• Sugar syrup is 170 ml of a total 1230 ml.
• Determine the percentage by splitting 170 with relation to 1230.

Split Approach Method

• 10% of 1230 is 123.
• Remaining value is 170 - 123 = 47.
• 1% of 1230 is 12.3.
• Since 47 is close to 4 times 12.3
• 4% approx.
• The final answer is around 10% + 3.8% ≈ 13.8%.

Alternative Percentage Calculation

• To find what percent 168 is of 1480, find 10% of 1480 which is 148
• Remaining value is 168 - 148 is 20.
• 1% of 1480 is 14.8.
• 0.5% is half of 14.8 which is 7.4.
• The total 1.5% is 22.2.
• This mean 1.4% is close enough, for an answer of approximately 11.4%.

Additional Resources

• HCF and LCM tests are available to test understanding of Highest Common Factor and Lowest Common Multiple.

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Data Interpretation Example with Percentages

• Review the revenue figures of Company A in 2018 (₹20.8) to understand how percentages are used with data in questions.
• Required to find 12% of 20.8. You can figure this out in your head without paper. Round 20.8 to 20. Then calculate 10% = 2 and 1% = approx .2. So 2% = .4. 2 + .4 = 2.4

Use of Percentages in Data Interpretation

• Find 28% of 32. Simplify math by turning 28% into 30% - 2%. 30% of 32 = 9.6 and subtract 2% of 32 = .64, for a total of 8.96, easily rounded to 9.

Multiplying Factors

• To find 10% of a number (X), multiply X by 0.1.
• To find 35% of a number, multiply by 0.35.
• To find 0.4% of a number, multiply by 0.004.
• To find 250% of a number, multiply by 2.5.
• To increase a number by 10%, multiply by 1.1.
• To increase a number by 4%, multiply by 1.04.
• To increase a number by 80%, multiply by 1.8.
• To increase a number by 150%, multiply by 2.5.

Effects on Decreasing Numbers

• To decrease a number by 20%, multiply by 0.8 (which is derived by calculating 100 - 20/100).
• A number can be decreased by a maximum of 100% (resulting in zero).

Rapid Percentage Work Through

• 3000% of 32.5 equals 32.5 multiplied by 30, or 325
• 8% of 4200 can be calculated.
• 120% of 330 requires adding 20% of 330 to it, resulting in 330 + 66 = 396.
• Find the value when 1050 is increased by 35% by finding 35% of 1050 and adding it to 1050.

Digital Sum Method

• Digital Sum Method to solve 135% of 1050: add the digits until one digit is left of 135 = 9
• add the digits until one digit is left of 1050 = 6: So 9 * 6 = 54 == 5+4 =9.. Any answer whose digits add up to 9 will be the correct answer.
• If given the problem of 50% of 18.24,. Turn the wording around to say , 18.24% of 50 for an answer of 9.12 .

Percentage Change

• An individual's salary of ₹52840 that increases 20% and then decreases 10%, the net change is 8% increase.
• Net percentage change can be calculated using the formula x + y + (xy/100), where x and y are the percentage changes.
• Determine that whether the person is salary is increased is determined using this formula .
• In scenario 1, follow this formula x + y + (xy/100) with x 20 and y is negative 10 . Results in the equation resulting is the number 8 : Resulting in the result in the formula being 8%
• In scenario 2, the value of the x and y variables in question is is 10 and 20 ( with 10 being negative , as the reduction comes first. Results in the same value: Therefor there is NO change. Formula in question therefore works in both directions , and the order does not matter

Increased Number

• If a value is first increased by 25% and then decreased by 20%, there is no net change, as these percentages negate each other.
• 100% increase followed by a 50% decrease results in no change.

Percentage Relationships

• If you increase a value by 1/n, decrease it by 1/(n+1) to revert to the original value.
• So 12.5% (1/8) increase is offset by a 11.11% (1/9) decrease.
• Multiplying x by 1.25 is the same as saying increase value, 25%
• 1.25 = (in fraction) 5/4
• Inversely reducing that value , means saying 4/5
• The percentage increase has to be 20% for for there to be no net change in this exchange:.

Comparing with Base Numbers

• When comparing a number "A" to another number "B," remember to keep "B" as the denominator in a percentage equation.

Complex Percentage Problems

• A is 33.33% more than D, B is 25% less than C, and A is 150% of B.
• What percentage is C of D?
• A is 1/3 of D
• B's value has been reduced by 25%
• A /B = 150%(of D) or 1.5 times

Fast Percentage Solution Methods

• The short cut method needs to provide something of an advantage
• There are other considerations for for example: the actual exam.

Box Approached Percent Solution

Example

• There is a class of students whose distribution is determined by 60% girls and 40 % boys
• There are 60 students available .
• The number of girls are therefore 24
• the number of boys are therefore 36
• Now to find the new equation where there have to be more girls added ..
• To the point that the school is now 30 boys to 70 girls .
• We can create a mental model and derive our numbers as , we are already given 30 percent has to 36 girls . From. there it is a short step to multiplying 36,3 and solving 100% from there ..
• The final number is .. 16 students , new to the class