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# the sum of numerator and denominator of a fraction is 8 . if 3 is added to both the numerator and denominator the fraction becomes 3/4 . find the fraction

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This is the basic and conceptual question from linear equations in two variables as it was already asked in various examinations in which we have been asked to find the fraction if the sum of numerator and denominator of a fraction is 8 . if 3 is added to both the numerator and denominator the fraction becomes 3/4 .

Kindly give me a detailed solution of this question

Book- RS Aggarwal, Class 10, chapter 3E, question no 19

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1. Let the required fraction be x/y .Â  Then, we have:

x + y = 8 â€¦â€¦(i)Â  And,

x+3/ y+3 = 3/4

â‡’4(x + 3) = 3(y + 3)

â‡’4x + 12 = 3y + 9

â‡’ 4x â€“ 3y = -3 â€¦â€¦(ii)

On multiplying (i) by 3, we get:

3x + 3y = 24

On adding (ii) and (iii), we get:

7x = 21

â‡’ x = 3

On substituting x = 3 in (i), we get:

3 + y = 8

â‡’ y = (8 â€“ 3) = 5

âˆ´ x = 3 and y = 5

Hence, the required fraction is 3/5

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