Question

The numerator of a fraction is four less than its denominator. If 1 is added to both, is numerator and denominator, the fraction becomes `1/2` Find the fraction.

Answer 1

Let the numerator of a fraction = x

and the denominator of a fraction = y

According to the condition,

x = y - 4      .....(i)

and `("x + 1")/("y + 1") = 1/2`

⇒ 2(x + 1) = y + 1

⇒ 2x + 2 = y + 1

⇒ 2x - y = -1     ...(ii)

Substitute the eq.(i) in eq.(ii)

2(y - 4) - y = -1

2y - 8 - y = - 1

y = - 1 + 8

y = 7

Now, put the value of y in eq.(i), we get

x = 7 - 4 = 3

∴ The numerator of a fraction is 3

and denominator is 7 and the fraction is `3/7`