Question

if the numberatior of a fraction is increased by 4 and the demominatio is decreased by 3 then the fraction becomes 2/3 and if both numberator and demonitor are increade by 5 then the fraction becomes 1/2 the orignal fraction is

Answer 1

The original fraction is
`(8)/(21)`.

Let the numerator be represented by x, and the denominator by y. So that;

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

`(x + 5)/(y + 5)` =
`(1)/(2)` ............ 2

From equation 1, we have;

2y - 6 = 3x +12

2y - 3x = 6 + 12

3x - 2y = -18.......................... 3

From equation 2, we have;

2x + 10 = y + 5

2x - y = -10 + 5

2x - y = -5 ....................... 4

Multiply equation 3 by 2, and equation 4 by 3 to have;

6x - 4y = -36 ........... 5

6x - 3y = - 15 ............. 6

subtract equation 6 from 5,

6x - 6x -4y + 3y = -36 + 15

-y = -21

y = 21

Substitute the value of y in equation 4,

2x - y = -5

2x - 21 = -5

2x = -5 + 21

2x = 16

x = 8

Thus, the original fraction is
`(8)/(21)`.