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If 1 is added to the denominator of a rational number, it becomes 1/2 whereas, 1 is added to the numerator of the rational number, it becomes 1. What is the Rational Number?

If 1 is added to the denominator of a rational number, it becomes 1/2 whereas, 1 is added to the numerator of the rational number, it becomes 1. What is the Rational Number? Correct Answer 2/3

Calculation

Let the number be 'p/q'

When 1 is added to denominator,

p/(q + 1) = 1/2

⇒ 2p = q + 1 ----(1)

When 1 is added to numerator,

(p + 1)/q = 1

⇒ p + 1 = q ----(2) 

From equation (1) and (2) we get,

2p = p + 2

⇒ p = 2

⇒ q = 3

∴ p/q = 2/3

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