Question
Sat December 01, 2012 By:

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.

Expert Reply
Sat December 01, 2012
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.
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