# If 2 is added to the numerator of a fraction it reduces to 1/2 and if 1 is subtracted from the denominator it reduces to 1/3. Find the fraction.

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Given that

x+2/y =1/2 -----> equ i

x/y-1 =1/3 -----> equ ii

From i and ii

2(x+2) =1(y) -------> equ i

3(x) =1(y-1) -------> equ ii

=> 2x+4=y

3x=y-1

Subtract i and ii. we get

2x - y = -4

3x - y = -1

(-) (+) = (+)

______________

-x = -3

_____________

=> x=3

subtitute x=3 in equ i. we get

2(3+2)=y

=> 2(5) =y

=> y=10

Therefore the value of x and y are 3 and 10 respectively.

= ...............(1)

= .................(2)

(1) ⇒ 2x+4 = y

⇒2x-y+4 = 0

(2) ⇒ 3x = y-1

⇒ 3x-y+1 = 0

solving the equations

3x-y+1 = 0

2x-y+4 = 0

---------------

x-3 = 0

x = 3

substitute x value in any of the above equation,

6-y+4 = 0

y = 10