# If 8 is added to the numerator of a fraction,its value becomes 2 If 5 is added to the denominator,the fraction becomes 1/5. By forming simultaneous equations and solving them,find the fraction....

If 8 is added to the numerator of a fraction,its value becomes 2

If 5 is added to the denominator,the fraction becomes 1/5.

By forming simultaneous equations and solving them,find the fraction.

Thanks

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### 1 Answer

Let fraction be `x/y` .

By given condition first ,we have

`(x+8)/y=2`

`x+8=2y` (i)

By given condition second

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

`5x=y+5`

`5x-5=y` (ii)

substitute y from (ii) in (i)

x+8=2(5x-5)

x+8=10x-10

8+10=10x-x

18=9x

x=2 (iii)

substitute x=2 in (ii)

y=5 ( 2) -5

y=10-5

y=5

**Thus fraction **`x/y=2/5`