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प्रश्न
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?
उत्तर
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`.
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