Question

a fraction becones 1/3 when 1 is subtracted from tge numerator and it becomes 1/4 when 8 is added to its denomintor find the fraction​

Answer 1

Step-by-step explanation:

Let the fraction be x/y, where x is the numerator and y is the denominator

Fraction becomes 1/3 when 1 is subtracted from the numerator

(x - 1)/y = 1/3

y = 3 (x - 1)

y = 3x - 3 ..Eq..1

It becomes 1/4 when 8 is added to its denominator.

x/(y + 8) = 1/4

Cross multiplication

(y + 8) = 4x

4x = y + 8….Eq 2

Substituting the value of y from Eq. 1 to Eq. 2

4x = y + 8

4x = 3x - 3 + 8

4x - 3x = 5

x = 5

The numerator is 5

Substituting the value of x in Eq. 2 to derive the value of y

4x = y + 8

4 × 5 = y + 8

20 = y + 8

y = 20 - 8

y = 12

The denominator is 12.

The fraction is 5/12

,Answer: the fraction Is 5/12

Now checking the correctness of answer by subtracting 1 from the numerator

Fraction is 5/12

(5–1)/12 = 4/12 = 1/3

Means answer is correct