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# Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:(ii) A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction. Q.4(2)

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The solution of exercise3.5 10th math of question no.4 part 2 how i solve this question. Its fraction type question so i am not able to solve this question Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:(ii) A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.

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1. Let the fraction be x/y.

So, as per the question given,

(x -1)/y = 1/3 =>Â 3x â€“ y = 3â€¦â€¦â€¦â€¦â€¦â€¦â€¦(1)

x/(y + 8) = 1/4Â  => 4x â€“y =8 â€¦â€¦â€¦â€¦â€¦â€¦..(2)

Subtracting equation (1) from (2) , we get

x = 5 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦.(3)

Using this value in equation (2), we get,

(4Ã—5)â€“ y = 8

y= 12

Therefore, the fraction is 5/12.

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