The denominator of a fraction is greater than the numerator by 5. If 2 is added to both the numerator and the denominator, the value of the fraction so obtained is 1/2. Find the original fraction.
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Let the numerator be ( x ) and denominator be ( x + 5 )
Fraction = ( x ) / ( x + 5 )
If 2 is added to both,
=> ( x + 2 ) / ( x + 7 ) = 1/2
=> 2( x + 2 ) = x + 7
=> 2x + 4 = x + 7
=> 2x - x = 7 - 4
= > x = 3
Hence,
Fraction = x / ( x + 5 ) = 3 / ( 3 + 5 )
Original fraction = 3/8
Fraction = ( x ) / ( x + 5 )
If 2 is added to both,
=> ( x + 2 ) / ( x + 7 ) = 1/2
=> 2( x + 2 ) = x + 7
=> 2x + 4 = x + 7
=> 2x - x = 7 - 4
= > x = 3
Hence,
Fraction = x / ( x + 5 ) = 3 / ( 3 + 5 )
Original fraction = 3/8
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