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MODULE - 2, , S.D.MEMORIAL CONVENT SCHOOL, , Commercial, Mathematics, , GANJKHWAJA CHANDAULI, Notes, , PERCENTAGE AND ITS APPLICATIONS, You must have seen advertisements in newspapers, television and hoardings etc of the, following type:, “Sale, up to 60% off”., “Voters turnout in the poll was over 70%”., “Ramesh got 93% aggregate in class XII examination”., “Banks have lowered the rate of interest on fixed deposits from 8.5% to 7%”., In all the above statements, the important word is ‘percent’. The word ‘percent’ has been, derived from the Latin word ‘percentum’ meaning per hundred or out of hundred., In this lesson, we shall study percent as a fraction or a decimal and shall also study its, applications in solving problems of profit and loss, discount, simple interest, compound, interest, rate of growth and depreciation etc., , OBJECTIVES, After studying this lesson, you will be able to, , , illustrate the concept of percentage;, , , , calculate specified percent of a given number or a quantity;, , , , solve problems based on percentage;, , , , solve problems based on profit and loss;, , , , calculate the discount and the selling price of an article, given marked price of, the article and the rate of discount;, , , , solve inverse problems pertaining to discount;, , , , calculate simple interest and the amount, when a given sum of money is invested, for a specified time period on a given rate of interest;, , Mathematics Secondary Course, , 203

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MODULE - 2, Commercial, Mathematics, , Notes, , Percentage and Its Applications, , , illustrate the concept of compound interest vis-a-vis simple interest;, , , , calculate compound interest, the amount and the difference between compound, and simple interest on a given sum of money at a given rate and for a given time, period; and, , , , solve real life problems pertaining to rate of growth and decay, using the formula, of compound interest, given a uniform or variable rate., , EXPECTED BACKGROUND KNOWLEDGE, , , Four fundamental operations on whole numbers, fractions and decimals., , , , Comparison of two fractions., , 8.1 PERCENT, 7, , 3, Recall that a fraction, , 4, , means 3 out of 4 equal parts., , means 7 out of 13 equal parts, , 13, , 23, , and, , 100, , means 23 out of 100 equal parts., 23, , A fraction whose denominator is 100 is read as percent, for example, , 100, , is read as, , twenty three percent., The symbol ‘%’ is used for the term percent., A ratio whose second term is 100 is also called a percent,, So,, , 33 : 100 is equivalent to 33%., 3, , Recall that while comparing two fractions,, , 1, , , we first convert them to equivalent, 5, 2, fractions with common denominator (L.C.M. of the denominators)., thus, , and, , 3 3 2  6 , and,   , 5 5 2 10, 1 1 5 5,   , 2 2 5 10, , Now, because 6  5, 10 10, , 204, , 3 1,  , 5 2, , Mathematics Secondary Course

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MODULE - 2, , Percentage and Its Applications, , Commercial, Mathematics, , We could have changed these fractions with common denominator 100 as, 3 3 20 60,  , , or 60%, 5 5 20 100, , Notes, , 1 1 50 50,   , or 50%, 2 2 50 100, and so,, , 3, , , , 1, , 5, , as 60% is greater than 50%., 2, , 8.2 CONVERSION OF A FRACTION INTO PERCENT AND, VICE VERSA, In the above section, we have learnt that, to convert a fraction into percent, we change the, fraction into an equivalent fraction with denominator 100 and then attach the symbol %, with the changed numerator of the fraction. For example,, 3 3 25  75  75 1  75% and,  , , 4 4 25 100, 100, , 4 4  4  16, 1, ,  16 ,  16%, 25 25 4 100, 100, Note: To write a fraction as percent, we may multiply the fraction by 100, simplify, it and attach % symbol. For example,, 4  4 100%  16%, , 25 25, Conversely,, To write a percent as a fraction, we drop the % sign, multiply the number by, 1, (or divide the number by 100) and simplify it. For example,, 100, 47, 1, , ,, 47%  47 , 100 100, , 45%  45, , 1, 100, , , , 17, 1, , ,, 17%  17 , 100 100, , 210 21, 45, 9,  ,,  , 210% , 100 20, 100 10, , Mathematics Secondary Course, , 3% , , x% , , x, , 3, 100, , ., , 100, , 205

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MODULE - 2, , Percentage and Its Applications, , Commercial, Mathematics, , 8.3 CONVERSION OF DECIMAL INTO A PERCENT AND, VICE VERSA, Let us consider the following examples:, Notes, , 35, 1, 0.35 ,  35 ,  35%, 100, 100, 4.7 , , 47, , , , 10, , 470, , 1, ,  470 , , 100, ,  470%, , 100, , 459 459  1, , , 0.459 ,  45.9%, 1000 10 100, 63  1, 63, , , 0.0063 ,  0.63%, 10000 100 100, Thus, to write a decimal as a percent, we move the decimal point two places to the, right and put the % sign, Conversely,, To write a percent as a decimal, we drop the %sign and insert or move the decimal, point two places to the left. For example,, 43% = 0.43, , 75% = 0.75, , 12% = 0.12, , 9% = 0.09, , 115% = 1.15, , 327% = 3.27, , 0.75% = 0.0075, , 4.5% = 0.045, , 0.2% = 0.002, , Let us take a few more examples:, Example 8.1: Shweta obtained 18 marks in a test of 25 marks. What was her percentage, of marks?, Solution:, , Total marks = 25, Marks obtained = 18,  Fraction of marks obtained =,  Marks obtained in percent =, , 18, 25, 18, , × 4  72 = 72%, 4 100, 25, , Alternatively:, 18, Marks obtained in percent =, , 206, , 25, , × 100% = 72%, , Mathematics Secondary Course

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MODULE - 2, , Percentage and Its Applications, Example 8.2: One-fourth of the total number of shoes in a shop were on discount sale., What percent of the shoes were there on normal price?, Solution:, , Fraction of the total number of shoes on sale =, , Commercial, Mathematics, , 1, 4, ,  Fraction of the total number of shoes on normal price = 1, , 1, 4, , , , 3, , Notes, , 4, , 3 25  75  75% or 3 100%  75%, , = , 4 25 100, 4, Example 8.3: Out of 40 students in a class, 32 opted to go for a picnic. What percent of, students opted for picnic?, Solution:, , Total number of students in a class = 40, Number of students, who opted for picnic = 32, ,  Number of students, in percent, who opted for picnic, 32, 100%  80%, =, 40, Example 8.4: In the word ARITHMETIC, what percent of the letters are I’s?, Solution:, , Total number of letters = 10, Number of I’s = 2,  Percent of I’s =, , 2, , 100%  20%, , 10, Example 8.5: A mixture of 80 litres, of acid and water, contains 20 litres of acid. What, percent of water is in the mixture?, Solution:, , Total volume of the mixture = 80 litres, Volume of acid = 20 litres,  Volume of water = 60 litres,  Percentage of water in the mixture =, , 60, , 100%  75%, , 80, , CHECK YOUR PROGRESS 8.1, 1. Convert each of the following fractions into a percent:, 12, (a), , 25, , 9, (b), , 20, , Mathematics Secondary Course, , 5, (c), , 12, , 6, (d), , 15, , 125, (e), , 625, 207

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MODULE - 2, , Percentage and Its Applications, , Commercial, Mathematics, (f), , 3, 10, , (g), , 108, 300, , (h), , 189, 150, , (i), , 72, 25, , (j), , 1231, 1250, , 2. Write each of the following percents as a fraction:, Notes, , (a) 53%, , (b) 85%, 3, , 7, (c) 16 %, 8, , (d) 3.425%, , (e) 6.25%

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(f) 70%, , (g) 15 %, (h) 0.0025%, 4, 3. Write each of the following decimals as a percent:, (a) 0.97, (b) 0.735, (c) 0.03, (f) 1.75, (g) 0.0250, (h) 3.2575, 4. Write each of the following percents as a decimal:, (a) 72%, (b) 41%, (c) 4%, (f) 410%, (g) 350%, (h) 102.5%, , (i) 47.35%, , (j) 0.525%, , (d) 2.07, (i) 0.152, , (e) 0.8, (j) 3.0015, , (d) 125%, (i) 0.025%, , (e) 9%, (j) 10.25%, , 5. Gurpreet got half the answers correct, in an examination. What percent of her, answers were correct?, 6. Prakhar obtained 18 marks in a test of total 20 marks. What was his, percentage ofmarks?, 7. Harish saves ` 900 out of a total monthly salary of ` 14400. Find his, percentage ofsaving., 8. A candidate got 47500 votes in an election and was defeated by his, opponent by a margin of 5000 votes. If there were only two candidates and, no votes were declared invalid, find the percentage of votes obtained by the, winning candidate., 9. In the word PERCENTAGE, what percent of the letters are E’s?, 10. In a class of 40 students, 10 secured first division, 15 secured second division, and 13just qualified. What percent of students failed.