the numerator fraction is 1 less than its denominator. if the numerator is increase bi fore and the denominator is increased by 5

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1. Question :-

   • The numerator of a fraction is 1 less than its denominator. If the numerator is increased by 4 and the denominator is increased by 5, the new fraction becomes equivalent to 4 by 5. What is the original fraction?​

   Answer :-

   • The original fraction is 4/5.

   To find :-

   • The original fraction.

   Solution :-

   Let the denominator of the original fraction be “x”.

   It is given that :-

   • The numerator of the fraction is 1 less than it’s denominator.

   Hence :-

   • The numerator of the original fraction will be “x – 1.”

   ——————————————-

   Increasing the numerator by 4,

   • We get “x – 1 + 4”.

   Increasing the denominator by 5,

   • We get “x + 5”.

   Now, it is given that :-

   • When the numerator is increased by 4 and the denominator is increased by 5, the new fraction becomes equivalent to 4/5.

   Therefore,

   [tex]\implies \sf \dfrac{x – 1 + 4}{x + 5} = \dfrac{4}{5}[/tex]

   [tex]\sf \implies 5 \: (x – 1 + 4) = x + 5 \: (4)[/tex]

   [tex]\sf \implies 5x – 5 + 20 = 4x + 20[/tex]

   [tex]\sf \implies 5x + 15 = 4x + 20[/tex]

   [tex]\implies \sf 5x – 4x = 20 – 15[/tex]

   [tex]\implies \underline{\boxed{\sf x = 5}}[/tex]

   ——————————————-

   Hence :-

   [tex]\rm Numerator = x – 1 = 5 – 1 = 4.[/tex]

   [tex]\rm Denominator = x = 5.[/tex]

   Thus, the original fraction is :-

   [tex]\underline{\boxed{\bf \dfrac{4}{5}}}[/tex]

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