Problem:
Two positive numbers x and y are in the ratio a:b, where 0<a<b. If x+y=c, then the smaller of x and y is
Answer Choices:
A. bac
B. bbc−ac
C. a+bac
D. a+bbc
E. b−aac
Solution:
Since y=abx,ab>1, and x>0, it follows that x is the smaller number. Also, x+y=c. Thus
x+abx=cax+bx=ac,x=a+bac