A fraction becomes 911, if 1 is added to both numerator and denominator. If 3 is added to both the numerator and the denominator it becomes 56. Find the fraction.
Let the numerator be x and the denominator be y.
From the given information, we have,
x+1y+1=911andx+3y+3=56or,x+1y+1=911=>11(x+1)=9(y+1)=>11x+11=9y+9=>11x−9y+2=0Also,x+3y+3=56=>6(x+3)=5(y+3)=>6x+18=5y+15=>6x−5y+3=0Thus,equationsare:11x−9y+2=06x−5y+3=0
Using cross-multiplication method,
x(−9)(3)−(2)(−5)=y(2)(6)−(3)(11)=1(11)(−5)−(6)(−9)x−27+10=y12−33=1−55+54x−17=y−21=1−1=>x−17=1−1or,x=17=>y−21=1−1or,y=21
Thus, original fraction is xy=1721