Answer:
The original fraction is 13/27
Step-by-step explanation:
Let the fraction be x/y. This means that the numerator is x and the denominator is y.
One-fifth of the sum of the numerator and the denominator of a particular fraction is 8. This means that
1/5 (x+y) = 8
Cross multiplying with 5,
x+y = 5×8 = 40 - - - - - - - -1
If the numerator is subtracted from 22, the original fraction becomes 1/3. This means that
(22-x)/y = 1/3
Cross multiplying with y and 3,
3(22-x) = y×1
66-3x = y - - - - - -2
Substituting y = 66-3x into equation 1, it becomes
x + 66 - 3x = 40
x -3x = 40-66
-2x = -26
x = 26/2 = 13
y = 40 - x = 40 - 13
= 27
The original fraction is 13/27
