The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3, they are in the ratio 2 : 3. Determine the fraction.

Question

Philoid · Accepted Answer

Let the fraction be x/y.

According to question -

x + y = 4 + 2x

⇒ - x + y = 4.....(1)

and,

On Cross multiplying, we get -

⇒ 3x + 9 = 2y + 6

⇒ 3x - 2y = - 3.....(2)

From equation (1), we get -

x = y - 4 .....(3)

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

3(y - 4) - 2y = - 3

⇒ y = 9

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

x = 5

Thus, the required fraction is 5/9.