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# Find a fraction which becomes ( 1/2 ) when 1 is subtracted from the numerator and 2 is added to the denominator, and the fraction becomes ( 1/3 ) when 7 is subtracted from the numerator and 2 is subtracted from the denominator.

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An important and exam oriented question from linear equations in two variables as it was already asked in various examinations in which we have given that when 1 is subtracted from the numerator, the fraction becomes 1/2 and when 2 is added to the denominator, and the fraction becomes ( 1/3 ) when 7 is subtracted from the numerator and 2 is subtracted from the denominator. And we asked to find the fraction

Kindly solve the above problem

RS Aggarwal, Class 10, chapter 3E, question no 22

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

xâˆ’1/ y+2 = 1/2

â‡’ 2(x â€“ 1) = 1(y + 2)

â‡’2x â€“ 2 = y + 2

â‡’2x â€“ y = 4 â€¦â€¦(i)

Again, xâˆ’7/ yâˆ’2 = 1/3

â‡’3(x â€“ 7) = 1(y â€“ 2)

â‡’3x â€“ 21 = y â€“ 2

â‡’ 3x â€“y = 19 â€¦â€¦(ii)

On subtracting (i) from (ii), we get:Â  x = (19 â€“ 4) = 15

On substituting x = 15 in (i), we get:Â  2 Ã— 15 â€“ y = 4

â‡’ 30 â€“ y = 4

â‡’y = 26

âˆ´ x = 15 and y = 26

Hence, the required fraction is 15/26

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