Question

The numerator of a fraction is 4 less than the denominator . If one is added to both its numerator and denominator it become 1/2 . Find the fraction

Answer 1

let numerator be x
now, x+1/x+5=1/2
        2x+2=x+5
        x=5-2=3 answer.

Answer 2

$\huge\tt\colorbox{blue}{Answer}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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Numerator is 4 less than denominator

If 1 is added to both then the fraction becomes 1/2

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

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Required fraction = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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Let the denominator be x

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Therefore numerator is x - 4

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Acc. to the question :-

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$\sf :\implies\:{\dfrac{x-4+1}{x+1} = \dfrac{1}{2}}$

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$\sf :\implies\:{\dfrac{x- 3}{x+1} = \dfrac{1}{2}}$

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$\sf :\implies\:{2 ( x - 3 ) = x + 1 }$

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$\sf :\implies\:{2x - 6 = x + 1 }$

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$\sf :\implies\:{2x - x = 6 + 1 }$

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$\sf :\implies\:{x = 7 }$

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Putting value of x in the fraction

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Numerator = x - 4 = 7 - 4 = 3

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Denominator = x = 7

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

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Required fraction = 3 / 7