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The numerator of a rational number is smaller than its denominator by 3 . If the numerator is decreased by 1 and the denominator is increased by 2 , the number becomes \( \frac{1}{3} \). Find the rational number. |
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Answer» Let the rational number be \(\frac ab\) According to given conditions, we obtain a = b - 3 ......(i) And \(\frac{a - 2}{b + 2} = \frac13\) ⇒ 3a - 3 = b + 2 ⇒ 3(b - 3) - 3 = b + 2 (From(i)) ⇒ 3b - 12 = b + 2 ⇒ 2b = 14 ⇒ b = 7 ∴ a = 7 - 3 = 4 Hence, required rational number is \(\frac47\). |
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