A variable x is proportional to y. If 3 values $$x_1, x_2, x_3$$ of x are in the ratio 2:3:4 such that $$x_1 + x_2 + x_3$$ = 9 and $$x_1y_1+x_2y_2+x_3y_3$$ = 29 then the ratio of the increase percentages of $$x_1y_1$$, $$x_2y_2$$, $$x_3y_3$$ over $$x_1,x_2,x_3 $$respectively is

$$x_1, x_2, x_3$$ of x are in the ratio 2:3:4.

Let say,$$x_1=2k,x_2=3k,x_3=4k$$

So,2k+3k+4k=9

or,k=1.

So,$$x_1=2,x_2=3,x_3=4$$

Now,

$$x_1y_1+x_2y_2+x_3y_3$$ = 29

or,$$2y_1+3y_2+4y_3$$ = 29.

By using trial and error, we can say that 

$$y_1=2,y_2=3 and y_3=4$$ can be the values.

so,$$x_1y_1=4,x_2y_2=9,x_3y_3=16$$.

So, required increments are 100%,200% and 300%.

So, required ratio is 100:200:300=1:2:3.

C is correct choice.