After One Year

#Problem 17

If a,b,c,d are positive real numbers then find a possible value of a/(a+b+d)+ b/(b+c+a) + c/(b+c+d) + d/(a+c+d)

(a)11/5 (b)17/3 (c)2 (d)11/9

Solution Scheme And Approach:

a/(a+b+d)+ b/(b+c+a) + c/(b+c+d) + d/(a+c+d)>a/(a+b+d+c)+ b/(b+c+a+d) + c/(b+c+d+a) + d/(a+c+d+b)=1

a/(a+b+d)+ b/(b+c+a) + c/(b+c+d) + d/(a+c+d)<a/(a+b)+ b/(a+b)+ c/(c+d)+ d/(c+d) =2

Hence the range of the expression is (1,2)

Only option (d) suffice the condition.