Question

The sum of the numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to 1/3. Then the fraction is

Answer 1

Let the numerator be a & denominator be b..

a+b= 18   
                                       .............(1)
a/b+2 =1/3

3a = b+2 

  a = (b+2)/3

Substitute this value in eq 1

a + b =18

(b + 2)/3 + b = 18

b + 2 + 3b = 18 × 3

4b + 2 =54   

      4b =54-2     

       4b = 52        

        b = 52/4

        b = 13

Substitute the value of y in eq 1

a + b=18

a + 13=18

a = 18- 13

a = 5

Hence required fraction = a/b = 5/13

☺ Hope this Helps ☺

Answer 2

Let the fraction be x/y where x is the numerator and y is the denominator.
According to condition,
x+y=18        .............(i)
and 
x/(y+2)=1/3
3x       =y+2
3x-y-2 =0     ..............(ii)
Solving (i) and (ii), 
x = - 4 and y = 22
thus required fraction is -4/22 or -2/11.
that's it. as simple as that.