Question

One-fifth of the sum of the numerator and the denominator of a particular fraction is8. If the numerator is subtracted from 22, the original fraction becomes 1/3. What is the original fraction?

Answer 1

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