Question

The sum of the numerator and the denominator of a fraction is 10. If 1 is added to both the numerator and the denominator, the fraction becomes 1/2. Frame equations for the same.

Answer 1

Answer:

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see the attachment for the solution..

Answer 2

$\huge\star\boxed{\mathfrak\pink{\underline{\underline{Answer}}}}\star$

$\textbf{Fraction\:=\: \dfrac{3}{7} }$

$\huge\star\star\boxed{\mathbb\red{\underline{\underline{GIVEN}}}}\star\star$

$\odot\:\:\textbf{The sum of the numerator and the}$

$\textbf{denominator of a fraction is 10. }$

$\textbf{If\:1\:is\:added\:to\:both\:the\:numerator\:and}$

$\textbf{the\:denominator,\:the\:fraction\:becomes}$

$\textbf{1/2.\:What\:is\:the\:fraction\:??}$

$\huge\star\star\star\boxed{\mathbb\green{\underline{\underline{TO\: CALCULATE}}}}\star\star\star$

$\odot\:\:\textbf{Numerator, Denominator and fraction}$

$\huge\star\star\star\boxed{\mathcal\red{\underline{\underline{Explanation}}}}\star\star\star$

$\textsf{Let the numerator and denominator be x and y respectively.}$

$\huge\texttt{ATQ,}$

$\huge\textsf{x+y=10 ............ (i) }$

$\huge\textsf{x=10-y ........... (ii)}$

$\huge\textsf{ \dfrac{x+1}{y+1}\:=\:\dfrac{1}{2} ............(iii)}$

$\huge\textsf{Cross multiplying the fraction}$

$\huge\textsf{ 2x+2=y+1 }$

$\huge\textsf{ x=\dfrac{y-1}{2} .......... (iv)}$

$\textsf{Substituting the value of x from (ii) in (iv)}$

$\huge\textsf{ 10-y=\dfrac{y-1}{2} }$

$\textsf{Cross multiplying the fraction, we get}$

$\huge\textsf{20-2y=y-1}$

$\huge\textsf{-3y=-21}$

$\huge\textsf{y=7}$

$\textsf{Substituting the value of y in (ii)}$

$\huge\textsf{x=3}$

$\huge\textbf{Numerator=3}$

$\huge\textbf{Denominator=7}$

$\huge\boxed{\therefore\textsf{Fraction= \dfrac{3}{7} }}$

$\huge\textbf{Answer\:is\: \dfrac{3}{7} }$

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