Question

Find a fraction which becomes 1 by 2 when 1 is subtracted from the numerator and 2 is added to the denominator and a fraction becomes 1 by 3 when 7 is subtracted from the numerator and 2 is subtracted from the denominator.

Answer 1

Let fraction be x/y
according to the question 
2x-y = 4 (1)
3x-y = 19 (2)
To solve equ (1) and equ (2), 
x = 15 
y = 26
Hence the fraction is 15/26

Answer 2

let the fraction be x
$x \div y$
case 1

$x - 1 \div y + 2 = 1 \div 2$
case 2.

$x - 7 \div y - 2 = 1 \div 3$