The denominator of a rational number is greater than its numerator by 3. If
numerator and denominator are increased by 1 and

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1. Answer:

   Correct Question :-

   The denominator of a rational number is greater than its numerator by 3. If numerator and denominator are increased by 1 and 4 respectively. The number obtained is ½. Find the rational number.

   Given :-

   The denominator of a rational number is greater than its numerator by 3. If numerator and denominator are increased by 1 and 4 respectively. The number obtained is ½.

   To Find :-

   What is the rational number.

   Solution :-

   Let, the numerator be x

   And, the denominator will be x + 3

   Then, the rational number is [tex]\sf \dfrac{x}{x + 3}[/tex]

   According to the question,

   ↦ [tex]\sf \dfrac{x + 1}{x + 3 + 4} =\: \dfrac{1}{2}[/tex]

   ↦ [tex]\sf \dfrac{x + 1}{x + 7} =\: \dfrac{1}{2}[/tex]

   By doing cross multiplication we get,

   ↦ [tex]\sf 2(x + 1) =\: 1(x + 7)[/tex]

   ↦ [tex]\sf 2x + 2 =\: x + 7[/tex]

   ↦ [tex]\sf 2x – x =\: 7 – 2[/tex]

   ➠ [tex]\sf\bold{\green{x =\: 5}}[/tex]

   Hence, the required rational number is :-

   ➲ [tex]\sf \dfrac{x}{x + 3}[/tex]

   ⇒ [tex]\sf \dfrac{5}{5 + 3}[/tex]

   ➦ [tex]\sf\bold{\purple{\dfrac{5}{8}}}[/tex]

   [tex]\therefore[/tex] The rational number is [tex]\sf\boxed{\bold{\red{\dfrac{5}{8}}}}[/tex].

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