10 CHAP

# 10 CHAP - 10.PERCENTAGE IMPORTANT FACTS AND FORMULAE 1...

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10.PERCENTAGE IMPORTANT FACTS AND FORMULAE 1. Concept of Percentage : By a certain percent ,we mean that many hundredths. Thus x percent means x hundredths, written as x%. To express x% as a fraction : We have , x% = x/100. Thus, 20% =20/100 =1/5; 48% =48/100 =12/25, etc. To express a/b as a percent : We have, a/b =((a/b)*100)%. Thus, ¼ =[(1/4)*100] = 25%; 0.6 =6/10 =3/5 =[(3/5)*100]% =60%. 2. If the price of a commodity increases by R%, then the reduction in consumption so asnot to increase the expenditure is [R/(100+R))*100]%. If the price of the commodity decreases by R%,then the increase in consumption so as to decrease the expenditure is [(R/(100-R)*100]%. 3. Results on Population : Let the population of the town be P now and suppose it increases at the rate of R% per annum, then : 1. Population after nyeras = P [1+(R/100)]^n. 2. Population n years ago = P /[1+(R/100)]^n. 4. Results on Depreciation : Let the present value of a machine be P. Suppose it depreciates at the rate R% per annum. Then,

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1. Value of the machine after n years = P[1-(R/100)] n . 2. Value of the machine n years ago = P/[1-(R/100)] n . 5. If A is R% more than B, then B is less than A by [(R/(100+R))*100]%. If A is R% less than B , then B is more than A by [(R/(100-R))*100]%. SOLVED EXAMPLES Ex. 1. Express each of the following as a fraction : (i) 56% (ii) 4% (iii) 0.6% (iv) 0.008% sol. (i) 56% = 56/100= 14/25. (ii) 4% =4/100 =1/25. (iii) 0.6 =6/1000 = 3/500. (iv) 0.008 = 8/100 = 1/1250. Ex. 2. Express each of the following as a Decimal : (i) 6% (ii)28% (iii) 0.2% (iv) 0.04% Sol. (i) 6% = 6/100 =0.06. (ii) 28% = 28/100 =0.28. (iii) 0.2% =0.2/100 = 0.002. (iv) 0.04%= 0.04/100 =0.004. Ex. 3. Express each of the following as rate percent : (i) 23/36 (ii) 6 ¾ (iii) 0.004 Sol. (i) 23/36 = [(23/36)*100]% = [575/9]% = 63 8/9%. (ii) 0.004 = [(4/1000)*100]% = 0.4%. (iii) 6 ¾ =27/4 =[(27/4)*100]% = 675%. Ex. 4. Evaluate :
(i) 28% of 450+ 45% of 280 (ii) 16 2/3% of 600 gm- 33 1/3% of 180 gm Sol. (i) 28% of 450 + 45% of 280 =[(28/100)*450 + (45/100)*280] = (126+126) =252. (iii) 16 2/3% of 600 gm –33 1/3% of 180 gm = [ ((50/3)*(1/100)*600) – ((100/3)*(1/3)*280)]gm = (100-60) gm = 40gm. Ex. 5. (i) 2 is what percent of 50 ? (ii) ½ is what percent of 1/3 ? (iii)What percent of 8 is 64 ? (iv)What percent of 2 metric tones is 40 quintals ? (v)What percent of 6.5 litres is 130 ml? Sol. (i) Required Percentage = [(2/50)*100]% = 4%. (ii) Required Percentage = [ (1/2)*(3/1)*100]% = 150%. (iii)Required Percentage = [(84/7)*100]% = 1200%. (iv) 1 metric tonne = 10 quintals. Required percentage = [ (40/(2 * 10)) * 100]% = 200%. (v) Required Percentage = [ (130/(6.5 * 1000)) * 100]% = 2%. Ex. 6. Find the missing figures : (i) ?% of 25 = 20125 (ii) 9% of ? = 63 (iii) 0.25% of ? = 0.04 Sol. (i)

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10 CHAP - 10.PERCENTAGE IMPORTANT FACTS AND FORMULAE 1...

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