The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.
Let the fraction =xy
First condition :
⇒x+y=2y−3
⇒x−y=−3
Second condition :
⇒x−1y−1=12
⇒2x−2=y−1
⇒2x−y=1
Subtract two equations ;
⇒2x−x=1+3⇒x=4
substitute in above equation
⇒y=1+8⇒y=7
∴ the fraction =47