The document contains examples of percentage calculations involving increases and decreases. It includes steps to solve problems where a price decreases by a certain percentage, candidates' vote totals are given with one receiving a percentage more than the other, and prices changing by different percentages to calculate the new difference. It also includes word problems involving percentages of groups, salary calculations, adulteration levels, and perimeter changes when dimensions increase and decrease by different percentages.

1. Percentages Teaching Notes – 2iim

4. 2) x x = Rs. 100 = Rs. 25 -> Drop = Rs. 75 -> Final price 3) x = Rs. 100 x = Rs. 400 -> Original price = Rs. 300 -> Final Price Soln:

5. In an election contested by two candidates, the winning candidate got 24% of the total votes more than the losing candidate. If the losing candidate got 76,000 votes, how many votes did the winning candidate get? Assume that there were no invalid votes? 4.

6. In an election contested by two candidates, the winning candidate got 24% of the total votes more than the losing candidate. If the losing candidate got 76,000 votes, how many votes did the winning candidate get? Assume that there were no invalid votes Let the losing candidate have x% votes and the winning candidate y% votes.  x + y = 100 and  y - x = 24. Subtracting the two equations , 2x = 76  x = 30  y = 62 38% = 76,000 62% = 76,000 * = 124,000 4

7. The price of Ford Fusion is 25% less than that of Honda City. By what percentage is a Honda City more expensive than a Ford Fusion? 5

8. The price of Ford Fusion is 25% less than that of Honda City. By what percentage is a Honda City more expensive than a Ford Fusion? Let the price of Honda City= x Price of Ford Fusion = x - 25% x = x - Difference in price = Percentage by which Honda City is more expensive than = * 100 = 33.33% 5.

9. 40% of the people in a gathering speak English. Of the remaining people, 60% speak Hindi. If 96 people speak neither Hindi nor English, how many people were there in the gathering? 6

10. 40% of the people in a gathering speak English. Of the remaining people, 60% speak Hindi. If 96 people speak neither Hindi nor English, how many people were there in the gathering? Let the total number of people in the gathering = x 24% x = 96 => x = 96 * = 400 x(100%) English 40% Non-English 60% Hindi 60% * 60% = 36% Non-Hindi 60% - 36% = 24% 6

11. Ann and Ron are a married couple and Ann earned twice as much as Ron in the month of January. In Feb Ann got a rise of 20% while Ron got a rise of only 10%. If both of them saved half their wages and the combined savings of the couple in the month of February is Rs.52,500, what is the salary of Ron in February? 7

12. Ann and Ron are a married couple and Ann earned twice as much as Ron in the month of January. In Feb Ann got a rise of 20% while Ron got a rise of only 10%. If both of them saved half their wages and the combined savings of the couple in the month of February is Rs.52,500, what is the salary of Ron in February? 7 Jan Feb Saving Ann 2X 2.4x Ron X 1.1x

13. X = 30,000 Ron in Feb = 1.1x = Rs. 33,000 Soln:

14. 50% of the students in a class that has 40% women students have got jobs during the recently concluded placement week. If 60% of the men in the class have got placements, what percentage of the women in class are yet to be placed? 8

15. 50% of the students in a class that has 40% women students have got jobs during the recently concluded placement week. If 60% of the men in the class have got placements, what percentage of the women in class are yet to be placed? 8 60*60% =36% Placed Not placed Men Women 60% 40% 50% 50% Placed Not placed Men Women 60% 40% 50% 30%

16. Soln: percentage of the women in class are yet to be placed = 36% 24% 14% 26% Placed Not placed Men Women 60% 40% 50% 30%

17. A sample of 40 liters of diesel is found to be adulterated to the extent of 20%. How many liters of pure diesel be added to the above mixture so that level of impurity stands reduced at 5%? 9

18. A sample of 40 liters of diesel is found to be adulterated to the extent of 20%. How many liters of pure diesel be added to the above mixture so that level of impurity stands reduced at 5%? 9 Or, x = 160 liters 40 l Pure petrol Impurity 32 l 8 l X liters 32 + x 8 l 40 + x

19. What is the percentage change in the perimeter of a rectangle whose length increases by 5% and width decreases by 15%? 10

20. What is the percentage change in the perimeter of a rectangle whose length increases by 5% and width decreases by 15%? Original perimeter = 2 ( l + b) New perimeter = 2 ( 1.05l + 0.85b) Change in perimeter = 0.1l -.3b With this, we cannot compute the percentage change in perimeter 10