Important Practice Questions on Percentages (Part 2)

Duration: 46 min

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This educational video features a lecture by Yash Jain Sir from Knowledge Gate Eduventures, focusing on advanced percentage calculation techniques and problem-solving strategies. The session begins with complex arithmetic problems involving percentages of decimals, utilizing shortcuts like squaring numbers ending in 5. The instructor then transitions to word problems involving voter demographics, library book categorization, and relative percentage changes between two quantities. Key formulas for net percentage change (x^2/100 for equal increase/decrease and x - y - xy/100 for unequal changes) are introduced and applied to various scenarios. The lecture concludes with a large-scale summation problem and a final review of net change concepts.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card "PERCENTAGE" and blue dice with percentage signs. The first question appears: "Q1: Find 19.5% of 1.95 + 24.5% of 245 - 14.5% of 1.45 ?". The instructor begins solving by writing (19.5/100) * 1.95 and then uses a shortcut for squaring numbers ending in 5, writing (195)^2. He explains that 19.5% of 1.95 is equivalent to (195/1000) * 1.95, which simplifies to (195)^2 / 100000.

  2. 2:00 – 5:00 02:00-05:00

    The instructor completes the calculation for Q1 using the square shortcut: (195)^2 = 38025, (245)^2 = 60025, (145)^2 = 21025. He adjusts decimal places to get 0.38025 + 60.025 - 0.21025. He then introduces Q2: "Find 10.5% of 105 + 12.5% of 125?". He calculates (105)^2 = 11025 and (125)^2 = 15625. He writes 10.5% as 105/1000.

  3. 5:00 – 10:00 05:00-10:00

    The instructor solves Q2 by converting 12.5% to 1/8, calculating 125/8 = 15.625. He then moves to Q3, a word problem about voters. He assumes total voters = 100, splits them into Party A (40) and Party B (60). He calculates 20% of Party A (8) and 75% of Party B (45) voting for Candidate A, summing to 53%. He draws a tree diagram to visualize the voter split.

  4. 10:00 – 15:00 10:00-15:00

    The instructor tackles Q4: "Find the value of 37.5 % of 64 + 62.5 % of 900 ?". He converts 37.5% to 3/8 and 62.5% to 5/8. He calculates 3/8 * 64 = 24 and 5/8 * 900 = 562.5, summing to 586.5. He emphasizes converting percentages to fractions for easier calculation.

  5. 15:00 – 20:00 15:00-20:00

    The instructor presents Q5, a complex library problem involving English, German, and French books, and sub-categories like fiction and non-fiction. He assumes a total of 300 books initially but realizes the numbers (like 10% of non-fiction) might not be integers, suggesting a need for a larger base number like 3000 to handle the 40% of autobiographies constraint. He draws a branching diagram to track the book categories.

  6. 20:00 – 25:00 20:00-25:00

    The instructor moves to Q6: "If A is 20% more than B, by what percent is B less than A?". He explains the relative percentage change concept, writing 100/120. He then solves Q7: "Sita has some money which is 10% less than Gita. By what percent is Gita's money more than Sita?", applying the same logic to find 11.11%. He writes the formula 100/100+p.

  7. 25:00 – 30:00 25:00-30:00

    The instructor solves Q8: "Bag A contains 40% more marbles than Bag B. What percent less marbles are contained in B as Compared to A?". He then moves to Q9, a team games problem. He sets up an equation where initial games = n, and new loss percentage is 25%, solving for n = 15 and total games = 20. He writes the equation (0.2n + 2) / (n + 5) = 0.25.

  8. 30:00 – 35:00 30:00-35:00

    The instructor solves Q10: "Find 105% of 80 + 115 % of 340 + 145 % of 1200 + 185 % of 2480 ?". He breaks down each percentage (e.g., 105% = 100% + 5%) and calculates the values: 84, 391, 1380, 2852. He shows the step-by-step addition for each term.

  9. 35:00 – 40:00 35:00-40:00

    The instructor introduces Q11 (labeled Q13): "A number first increases by 18% and then decreases by 18%". He uses the formula x^2/100 to find the net decrease of 3.24%. He then solves Q12 with 12% increase and decrease, finding a 1.44% decrease. He writes the formula x^2/100 on the board.

  10. 40:00 – 45:00 40:00-45:00

    The instructor solves Q15: "A number first increases by 10% and then decreases by 5%". He uses the formula x - y - xy/100 to find a net increase of 4.5%. He writes the formula x - y - xy/100 on the board.

  11. 45:00 – 45:59 45:00-45:59

    The video concludes with a "THANKYOU FOR WATCHING" slide.

The lecture systematically builds from basic percentage calculations to complex word problems, emphasizing shortcuts and formulaic approaches. The progression moves from arithmetic manipulation (squaring numbers, fraction conversion) to logical deduction (voter demographics, library categorization) and finally to algebraic reasoning (relative percentage change, net change formulas). This structure helps students master both computational speed and conceptual understanding of percentage relationships.

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