Question

If the numerator of a fraction is increased by 2 and denominator is decreased by 1, it becomes `2/3`. If the numerator is increased by 1 and denominator is increased by 2, it becomes `1/3`. Find the fraction.

Answer 1

Let the numerator and denominator a fraction be x and y respectively .
According to the question,
`[ x + 2 ]/[ y - 1 ] = 2/3`
3x + 6 = 2y - 2
3x - 2y = - 8                               ........(1)
And,
`[ x + 1 ]/[ y + 2 ] = 1/3`
3x + 3 = y + 2
3x - y = - 1                                  .......(2)
Now,
Subtracting equation (1) from (2),
     3x - y = - 1
-   3x - 2y = - 8 
    -     +      +   
            y = 7

From (1) ,
3x - 2 (7) = - 8
3x = - 8 + 14
x = 2
Required fraction = `2/7`