DAY-1 || PERCENTAGE (प्रतिशतता) || Basic Concepts ❤️ ||All Govt Exams || BY ADITYA SIR || CGL TOPPER

Summary

The video is the first lesson in a basic percentage series. Aditya Ranjan introduces percentage as a foundational topic for competitive-exam arithmetic, then teaches conversions, mental-calculation techniques, and examples involving units and algebraic expressions.

1. Meaning of percentage and basic conversions

• Percent means “per 100.”
• To convert a percentage to a fraction, remove the percent sign, place the number over 100, and simplify.
  • Example: (20\% = 20/100 = 1/5).
• To convert a fraction to a percentage, multiply it by 100 and add the percent sign.
  • Example: (1/4 \times 100 = 25\%).

These two conversion rules are presented as essential basics for solving percentage questions.

2. Memorize common fraction-to-percentage values

The teacher recommends learning common fractions—especially from (1/1) through (1/20)—so they can be recognized quickly in exam questions. Examples include:

• (1/2 = 50\%)
• (1/3 = 33\frac{1}{3}\%)
• (1/4 = 25\%)
• (1/5 = 20\%)
• (1/6 = 16\frac{2}{3}\%)
• (1/7 \approx 14.28\%)
• (1/8 = 12.5\%)
• (1/9 = 11\frac{1}{9}\%)
• (1/10 = 10\%)
• (1/16 = 6.25\%)

Knowing these values, including useful decimal equivalents, can make calculations much faster.

3. Quickly convert fractions near whole numbers

When a fraction’s numerator is close to a multiple of its denominator, write it as a whole number plus or minus a familiar fraction:

• If the numerator is one more than a multiple of the denominator, split the fraction into a whole-number part plus (1/d).
  • Example: (9/8 = 1 + 1/8 = 112.5\%).
• If the numerator is one less than a multiple of the denominator, subtract (1/d) from the whole-number part.
  • Example: (7/8 = 1 - 1/8 = 87.5\%).
• This also works when the numerator is one more or less than a larger multiple. For instance, (17/8 = 2 + 1/8 = 212.5\%).
• For other improper fractions, divide the numerator by the denominator and express the result as a mixed number before converting to a percentage.

4. Break percentages into convenient parts

Instead of multiplying a number by a difficult percentage directly, split the percentage into easier components.

For example, (111\% = 100\% + 10\% + 1\%). To find (111\%) of 500:

• (100\%) of 500 = 500
• (10\%) of 500 = 50
• (1\%) of 500 = 5
• Total = 555

The same approach can be used with other convenient decompositions, such as (50\% + 14.28\%).

5. Use the symmetry rule for “percent of”

A useful identity is:

[ a\% \text{ of } b = b\% \text{ of } a ]

This can turn a difficult-looking calculation into an easier one. For example, (800\%) of 87.5 can be evaluated as (87.5\%) of 800.

6. Compare quantities by forming a ratio

To find what percentage one quantity is of another:

1. Make sure both quantities are in the same units.
2. Divide the first quantity by the second.
3. Multiply the result by 100.

The teacher also stresses comparing values through their ratio rather than unnecessarily calculating each value separately. If one value is (3/2) of another, for example, it is 50% greater than the other.

7. Convert units before finding a percentage

A percentage comparison requires quantities to use the same units. The lesson reviews the metric sequence:

milli – centi – deci – meter – deca – hecto – kilo

• Moving from a larger unit to a smaller unit: multiply by 10 for each step.
• Moving from a smaller unit to a larger unit: divide by 10 for each step.
• Example: To compare 80 metres with 5 kilometres, first convert 5 kilometres to 5,000 metres. Then (80/5{,}000 \times 100 = 1.6\%).

8. Work carefully with decimals

• To convert a decimal number to a percentage, multiply by 100. For example, (2.4 = 240\%).
• When dividing by 10, 100, or 1,000, shift the decimal point left by one, two, or three places, respectively.
• When adding or subtracting decimals, line up the decimal points. Trailing zeros can be added as needed.

9. Treat “of” as multiplication in equations

In percentage expressions, “of” means multiplication. The teacher demonstrates rearranging percentage equations by applying the same operations to both sides and simplifying. This can help express one percentage quantity in terms of another without calculating every value separately.

10. Use digit sums only as an option-checking aid

The lesson introduces the digit sum—adding the digits of a number—as a quick way to test or eliminate answer options in some multiple-choice calculations. This is a shortcut for checking possibilities, not a substitute for verifying the calculation: different numbers can have the same digit sum.

11. Exam preparation and closing remarks

The teacher says percentage is important across competitive exams and can support work in other arithmetic topics. He identifies himself as Aditya Ranjan and cites his exam experience and scores as part of his introduction. He closes by encouraging students to attend the continuing lessons and briefly announces other classes and courses.

Speakers and sources featured

• Aditya Ranjan — the identifiable speaker and mathematics instructor.
• SelectionWay SSC / Rankers Gurukul — the channel and learning platform associated with the lesson.
• Anil Sir — mentioned in a closing announcement about English classes; he is not heard speaking in the supplied subtitles.
• The instructor refers to questions from exams including SSC CGL, CHSL, CPO, MTS, Delhi Police, Railway, and banking exams.