Question

A fraction reduce to 1/4
when 2 is subtracted numerator and 3 is added to the
denominator but
them as reduce to 2/3 when 6 is added to numerator and denominator is multiplied by
3. Find the friction ​

Answer 1

let the numerator be X.

let the denominator be Y.

fraction = x/y.

according to question,

x-2/y+3 = 1/4.......(1)

x+6/ 3y = 2/3....... (2)

form (1) we have,

x-2/y+3 = 1/4

on cross multiplying we have,

4(x-2) = y+3

4x-8 = y+3

4x = y+3+8

4x = y+11

x = y+11/4 ...... (3)

on substituting (3) in (2) we have

x+6/ 3y = 2/3

y+11/4+6/3y = 2/3

taking LCM of R.H.S.,

3y+33y+24y/12y = 2/3

adding all the 'y' terms.,

60y/12 y = 2/3

3(60y) =2(12y)

180y = 24y

y= 24y/180

y= 2y/ 15

hence required fraction is

2/15

hop e it will help