the sum of the numerator and denominator of a fraction is 8. if the denominator is increased by 2 the fraction reduce to 1/3. find

1 thought on “the sum of the numerator and denominator of a fraction is 8. if the denominator is increased by 2 the fraction reduce to 1/3. find”

1. Answer:

   Let the numerator be x and the denominator be y.

   From the given information, we have,

   x+y=18and

   y+2

   x

   =

   3

   1

   or,x+y=18

   =>y=18−x….(i)

   Also,

   y+2

   x

   =

   3

   1

   =>3x=y+2

   =>3x−y−2=0….(ii)

   Solving by substitution method,

   Substituting (i) in (ii), we get,

   3x−y−2=0

   =>3x−18+x−2=0

   =>4x=20

   =>x=5

   Putting x=5 in equation (i), we get,

   y=18−x

   =>y=18−5

   =>y=13

   Thus, the original fractyion is

   y

   x

   =

   13

   5

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