The sum of the numerator and denominator of a fraction is 8. If 3 is added to both of the numerator and the denominator, the fraction becomes . Find the fraction.

Question

Philoid · Accepted Answer

Let the fraction be x/y.

According to question -

x + y = 8.....(1)

and,

On Cross multiplying, we get -

⇒ 4x + 12 = 3y + 9

⇒ 4x - 3y = - 3.....(2)

From equation (1), we get -

x = 8 - y.....(3)

Substituting the value of x in equation (2), we get -

4(8 - y) - 3y = - 3

⇒ 7y = 35

∴ y = 5

substituting the value of y in equation (3), we get -

x = 3

Thus, the required fraction is 3/5.