The Numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator becomes eight times the numerator, then find the fraction.

Let denominator of fraction = x
Then, numerator = x - 4
∴ Fraction = x - 4/x
Now, according to the question,
8[(x - 4) - 2] = (x + 1)
(x -4) - 2= (x + 1)/8
⇒ x - 6 = x + 1/8
⇒ 8x - 48 = x + 1
⇒ 8x - x = 48 + 1
⇒ 7x = 49
⇒ x = 49/7
∴ x = 7
∴ Fraction = (x - 4)/x
Put the value of x.
∴ Fraction = (7 - 4)/7 =3/7