PercentageTo change a fraction to a percent, find its decimal form, multiply by 100 and add a percent sign.Example: Express as a percent.Solution: to convert to a decimal, divide 3 by 8; this gives us 0.375. Multiplying 0.375 by 100 gives us 37.5%.To change a percent to a fraction, drop the percent sign and divide the number by 100. Example: Express 17% as a fraction.Solution: Dropping the % sign gives us 17, and dividing by 100 gives us = 0.17.Type 1:Formula:Verbal Mathematical

WhatP

Is=

%1/100

Of X

What is 10% of 20% of 30% 4000?Solution: P = 10 20 30 4000 = 24

Practice1. What is 3% of 5?a) b) c) d) 2. 5 percent of 55?a) .05b) .25 c) .50 d) .103. What percent of 20 is 16?a) 80%b) 65%c) 45% d) 804. What is .05 percent of 6.5?a) .13b) .013c) .325 d) .003255. If Y% of x = 29, then x = ?a) 2900b) c) d) 6. If bans point are defined so that 1 percent is equal to 100 bans points, then 82.5 percent is how many bans points greater than 62.5 percent?a) .02b) .2c) 200 d) 2007. B and C are points on the straight line AD, on which AB = BC = CD. What percent of AC = AD?a) 50%b) 66.67% c) 133.33% d) 150%Type 2: Formula: F = First Change, S = Second changeExample: The length and breadth of a room are decreased by 20% and 25% respectively. What is the corresponding decrease in the floor area of the room?Solution: - 20 25 + = - 40Example: If the each side of a square increases by 40%, then the area of the square increased by?Solution: 40 + 40 + = 96

Example: The radius of a circle is decreased by 5%, then the is decreased by Solution: - 5 5 + = - 9.75

Example: Successive discount of 10% and 20% is equal to single discount - 10 20 + = - 28

Practice:1. If the length of a rectangle is increases by 40% and the width is decreased by 20% the area of the rectangle will increase bya) 20%b) 12% c) 8% d) None2. If the side of a square decreased by 20%, then its area decreased by what percent?a) - 36%b) 44% c) 40% d) 36%3. If each side of a square increased by 30%, then the area of the square increases bya) 350%b) 200% c) 150% d) 120%4. If the area of the square increased by 44%, the side of the square is increases by a) 40%b) 30% c) 20% d) 69%5. The price of Sugar in 199 increased by 10% from in 1993. In 1995 the price decreased by 5% from that in 1994. In 1995 what is the increase in price with respect to price in 1993?a) 4%b) 4.5% c) 5% d) 5.5%6. In the DSE, the price of Bata Share rose 30% yesterday and fell 20% today. What is the total rise on fall in percentage?a) 10% riseb) 4% fall c) 4% d) 10% fall

Type 3: Mix %If 50% of the workers are graduates and of them 20% male, what percent of the workers are male and graduate?Formula: Mix % = = = 10

Practice1. In a certain class 40% of the students are girls and 20% of the girls wear glasses. What percent of students in the class are girls who wear glasses?a) 6%b) 8% c) 20% d) 16%

Type 4: % & Dual with given numberQ:A class of 10 girls and 20 boys arranged a picnic. However, only 15% of the girls and 30% of the boys attended the picnic. What percent of the class attended the picnic?Formula: = = 25

Practice1. In a class of 80 Students, 25% are girls. If 10% of the boys and 20% of the girls attended a picnic, what percent of the class did attend?a) 10%b) 12% c) 12.5% d) 120%

Type 5: % & Consumption changeQ:Price of paper has increased by 40%. How much paper usage must be curtailed so that expenditure for paper remain the same?Formula: = = 28.57%Q:Price of paper has decreased by 40%. How much paper usage must be increased so that expenditure for paper remain the same?Formula: == 66.67%

Practices1. The length of a rectangle is increased by 50%. By what percent would the width have to be decreased to maintain the same area?a) 33.33%b) 45% c) 50% d) 66.67%2. Price of paper has decreased by 30%. How much paper usage must be enhanced sot that expenditure for paper remain the same:a) 28.57%b) 23.33% c) 24.33% d) None3. The price of the sugar has increased by 60%. In order to restore the original price, the new price must be reduced by a) 33.33%b) 35% c) 37.5% d) 60%

Type 6:The price of a newspaper rises from Tk. 10 to Tk. 20. What is the percent increase in price?Formula: % Change = = = 100%

Practices1. If the price of a good increased from Tk. 30 to Tk. 42, find the percentage increase in the price?a) 12%b) 20% c) 40%d) 45%2. If the value of XYZ company stock drops from 25 per share to 21 per shares; what is the percent of the decrease?a) 4b) 8 c) 12 d) 16

Miscellaneous Problems:Class Practice:1. As salary is 125% of Bs salary. Cs salary is 80% of Bs Salary. The total of all three salaries is 61000. What is Cs Salary?a) $15,000b) $16,000c) $ 17,000d) $18,0002. If 8% tax on a sale amount to 96 paisa, what is the final price of the item?a) 1.20b) 2.60 c) 12.96 d) 6.363. Among the 100 students in a business school, 50% enrolled in a marketing course, of the enrolled students, 90% took the final exam. Two-third of the students who took the final exam passed it. How many students failed in the exam?a) 5b) 10 c) 15 d) 304. A Salesman gets a salary of Tk. 4500 per month plus 1.25% commission on the sales Tk. Amount he achieves in the month. How much sales, in Lakh Tk., he has to achieve in a month in order to get a total income of Tk. 7500 including his salary in the month?a) 3b) 3.6 c) 2.4 d) 5.65. A student first reduced a number by 20% and then increased it again by 20%. If the difference between the last number and the original number is 8, then the original number was?a) 200b) 250 c) 300 d) 4506. The price of a shirt increases from Tk. 350 to Tk. 700, the old price is what percent of the new price?a) 60%b) 50% c) 75% d) 200%7. If a jar contains 16 black marbles and 24 red marbles, what percent of all marbles in the jar are red?a) 33.33%b) 40% c) 60% d) 66.66%8. 8 % expressed as a fraction is:a) b) c) d) 9. 0.025 in terms of rate percent is:a) 25b) 2.5 c) 0.25 d) 37 10. What % of 250+ 25% of 68 = 67?a) 10b) 15 c) 20 d) 25

Home Assignment1. If 8% of x = 4% of y, then 20% of x is:a) 10% of yb) 16% of y c) 80% of y d) None of these2. If 37 % of a number is 900, then 62% of the number is:a) 1200b) 1350 c) 1500 d) 5403. Subtracting 6% of x from x is equivalent to multiplying x by how much?a) 0.94b) 9.4c) 0.094 d) 944. The price of an article is cut by 10%. To restore it to the former value, the new price must be increased by: a) 10b) 9 c) 11 d) 115. After deducting a commission of 5% a T.V. set costs Tk. 9595. Its gross value is:a) 10000b) 10074.75 c) 10100 d) None6. In an examination 65% of the total examinees passed. If the number of failures is 420, the total number of examinees is:a) 567b) 693 c) 1000 d) 12007. If As salary is 30% more than Bs, then how much percent is Bs salary less than As?a) 30b) 25 c) 23 d) 33 8. If 75% of a number is added to 75, the result is the number itself. Then, the number is:a) 400b) 30 0c) 60 d) 509. Subtracting 40% of a number from the number, we got the result as 30. The number is: a) 28b) 50 c) 52 d) 7010. A student has to ensure 40% marks to pass. He gets 178 marks and fails by 22 marks. The maximum marks are: a) 200b) 500 c) 800 d) 1000