# The sum of the numerator and the denominator of a fraction is 3 less than twice the denominator. If the numerator and the denominator are decreased by 1, the numerator becomes haljf the denominator. Determine the fraction.

let the fraction be x / y

then acc. to ques.

x + y + 3= 2y

x = y - 3 ............. (i)

also

x-1/y-1 =  y/2y = 1/2

x - 1 =( y-1) / 2

x = ( (y - 1) / 2 ) +1

x = (y +1) / 2

2x = y + 1

2x - y = 1 ............... (ii)

Subtituting the value of  (i)  in (ii) we have

2 ( y - 3 ) - y =1

2y - 6 -y = 1

y - 6 = 1

y = 7

x = y - 3

x = 7 - 3

x  = 4

Therefore the fraction is x / y = 4 / 7

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