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Class 10 > Learn Mathematics > If x:y = 9:10, find the value of (5x + 3y) : (5x - 3y)?
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If x:y = 9:10, find the value of (5x + 3y) : (5x - 3y)?

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The answer is 5:1. SOL :- x : y=9 : 10==> 10 x=9 y==> 5 x = 9 y/2, substituting 9y/2 for 5x in ( 5 x + 3 y) : (5 x - 3 y) gives 5: 1
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(5x + 3y) : (5x - 3y)=(5x/y+3):(5x/y-3) =(5*9/10+3):(5*9/10-3) =15/3=5
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x : y = 9:10 Or, x/y = 9/10 (5x + 3y) / (5x -- 3y) = (5x/y + 3) / (5x/y -- 3) = (5×9/10 +3)/(5×9/10 -- 3) = (9/2 + 3)/ (9/2 -- 3) = / = (15/3)/(3/3) = 15/3 = 5/1 = 5 Ans.
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Spoken English, Mathematics and Science tutor with 20+ years of experience

x/y=9/10 5x+3y/5x-3y = 5(x/y) +3 / 5(x/y) - 3
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Gourav Khandelwal

Using the Componend and Dividend Theorems: (x/y)=(9/10). (Given) Multiplying the given equation by 5 and dividing by 3 we get:- (5x/3y)=(3/2) Applying the theorem: (a/b)=(c/d) on transforming becomes ((a+b)/(a-b))=((c+d)/(c-d)). Therefore, ((5x+3y)/(5x-3y))=((3+2)/(3-2)) ((5x+3y)/(5x-3y))=5. (Answer)
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Given that x : y = 9 : 10. (x/y) = (9/10). now (5x + 3y) : (5x - 3y) = ? Dividing both Nr and Dr by y we (5x/y + 3y/y)/5(x/y) - 3(y/y) = / = /5(9/10) - 3] =/. taking LCM on Nr. and Dr., we get:- =/(45 - 30)/10 = (75/10)/(15/10) = (75/10) * (10/15) =75/15 = 5. Therefore (5x +3y) : (5x - 3y) = 5 : 1.
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Given that x : y = 9 : 10. (x/y) = (9/10). now (5x + 3y) : (5x - 3y) = ? Dividing both Nr and Dr by y we (5x/y + 3y/y)/5(x/y) - 3(y/y) = [5(x/y) + 3]/[5(x/y) - 3(y/y)] = [5(9/10) + 3]/5(9/10) - 3] =[(45/10) + 3]/[(45/10) - 3]. taking LCM on Nr. and Dr., we get:- =[(45 + 30)/10]/(45 - 30)/10 = (75/10)/(15/10) = (75/10) * (10/15) =75/15 = 5. Therefore (5x +3y) : (5x - 3y) = 5 : 1. read less
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