Question

what will be the fraction if
the sum of the numerator and denominator of a fraction is 18 if the numerator is decrease by 2 and denominator is increased by 2 the fraction reduces to 1 /5.

Answer 1

let the fraction be, x/y
where the numerator = x
                 denominator = y
according to the question,
x +y = 18
y = 18 -x...........(1)
and also,
(x -2)/ (y +2) = 1/5.........(2)
substitute (1) in (2),
(x-2)/ (18-x-2) =1/5
(x-2)/(20-x) = 1/5
5x- 10 = 20- x
5x +x = 20 +10
6x = 30
 x= 5
if x = 5 , 5 + y =18
             ⇒ y = 13
therefore, the fraction is 5/13