Question

If numerator is 2 less than denominator of a rational number and when 1 is subtracted from numerator and denominator both, the rational number in its simplest form is `1/2`. What is the rational number?

Answer 1

Suppose denominator of a rational number be x.

Numerator = Denominator – 2 = x – 2

According to the question,

`((x - 2) - 1)/(x - 1) = 1/2`

⇒ 2(x – 2 – 1) = x – 1

⇒ 2(x – 3) = x – 1

⇒ 2x – 6 = x – 1

⇒ 2x – x = 6 – 1

∴ x = 5

Hence, denominator = 5 and numerator = 5 – 2 = 3

Thus, the rational number is `3/5`.