[k42490]

you have 2 distinct gaseous compunds made from elements x and y:
compund 1: 30.43%x, 69.57%y
compund 2: 63.64%x, 36.36%y

when you react gas x with y, you get:
1 volume gas x + 2 volumes gas y -> 2 volumes compund 1

2 volumes gas x + 1 volume gas y -> 2 volumes compund 2

Assume simplest possible formula and determine relative atomic masses of element x and element y.

i don't understand how to incorporate the percents.
 

[DevaDevil]

I assume you should read the % as mass%

So then you read it as follows:
compound 1 : 1 gram comp. 1 is built up by 0.3043 grams X and 0.6957 grams Y

similar for compound 2

you then have mole fractions and mass fractions of X and Y for both compounds, and are able to calculate the fraction atomic mass X/atomic mass Y