Question

The denominator of a fraction exceeds its numerator by 3. If one is added to both numerator and denominator, the difference between the new and the original fraction 1/24 find the original fraction.

Answer 1

let Numerator=X

Therefor denominator=X+3

Fraction=X/(X+3)

New fraction=(X+1)/(X+4)

According to given condition

(X+1)/(X+4)-X(X+3)=1/24

taking the LCM and cross multiplying

24((X+1)*(X+3)-X*(X+4))=(X+3)(X+4)

or, 24*3=X^2+7X+12

or, X^2+7X-60=0

or, X^2+12X-5X-60=0

orX(X+12)-5(X+12)=0

or, (X-5)(X+12)=0

or, X=5 or -12

X can not be -12

therfor the original fraction is 5/8.

hope it helps..