Question

The numerator of a fraction is 3 less than its denominator. If 3 is subtracted from both the numerator and the denominator the fraction becomes 1/4.
Find the fraction.

Answer 1

Answer :-

The required fraction is 4/7.

Solution :-

Let the denominator of a fraction be x

Numerator of a fraction = 3 less than the denominator = 3 less than x = (x - 3)

According to the question :

⇒ {(x - 3) - 3}/{x - 3} = 1/4

⇒ (x - 3 - 3)/(x - 3) = 1/4

⇒ (x - 6)/(x - 3) = 1/4

By Cross multiplication

⇒ 4(x - 6) = 1(x - 3)

⇒ 4x - 24 = x - 3

⇒ 4x - x = - 3 + 24

⇒ 3x = 21

⇒ x = 21/3

⇒ x = 7

i.e Denominator of the fraction = 7

Numerator of the fraction = (x - 3) = (7 - 3) = 4

Fraction = Numerator/Denominator = 4/7

Therefore the required fraction is 4/7.

Answer 2

Solution :

Let, the fraction be x / y , where both x and y are integers.

ATQ,

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

and (x - 3) / (y - 3) = 1 / 4

or, 4 (x - 3) = y - 3

or, 4x - 12 = y - 3

or, 4 (y - 3) - 12 = y - 3 , by (i)

or, 4y - 12 - 12 = y - 3

or, 4y - 24 = y - 3

or, 4y - y = 24 - 3

or, 3y = 21

or, y = 7

From (i), we get

x = 7 - 3

or, x = 4

Therefore, the required fraction is 4/7