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=ab​x,ab​>1, and x>0, it follows that x is the smaller number. Also, x+y=c. Thus
​x+ab​x=cax+bx=ac,x=a+bac​​