Question

the denominator of a fraction is 4 more than the numerator if 1 is added to the numerator rater and 2 is added to the denominator the value of the functions become 4/5 find the original fraction​

Answer 1

Answer:-

Let the fraction be x/y.

Given:

Denominator is 4 more than the numerator.

⟶ Denominator = Numerator + 4

⟶ y = x + 4 -- equation (1)

Also,

If one is added to numerator and 2 is added to denominator, the fraction becomes 4/5.

$\implies \sf \: \frac{x + 1}{y + 2} = \frac{4}{5}$

Substitute y's value from equation (1).

$\implies \sf \: \frac{x + 1}{x + 4 + 2} = \frac{4}{5} \\ \\ \implies \sf \:5(x + 1) = 4(x + 6) \\ \\ \implies \sf \:5x + 5 = 4x + 24 \\ \\ \implies \sf \:5x - 4x = 24 - 5 \\ \\ \implies \sf \large{x = 19}$

Substitute the value of x in equation (1).

⟶ y = 19 + 4

⟶ y = 23

Therefore, the required fraction x/y is 19/23.