# Linear Equation 25

### From Homeworkwiki

**If the numerator of a fraction is decreased by 1, its value becomes 2 /3, but if the denominator is increased by 5,**

**its value becomes 1 / 2. What is the fraction ?**

**Solution:** Let the fraction be x / y

Therefore, (x - 1) / y = 2 / 3 and x / (y + 5) = 1 / 2

=> 3 x - 3 = 2 y and 2 x = y + 5

=> 3 x - 2 y = 3 and 2 x - y = 5

On solving, we get : x = 7 and y = 9

Therefore, **the required fraction = 7 / 9**