What is a simple ratio in which atoms combine? According to Modern Atomic Theory:


  The ratio in which the different atoms combine may be fixed and integral but may not always be simple.


The example given is that in sugar molecule the ratio of $\ce{C,H}$ and $\ce{O}$ atoms is $12:22:11$ which is not simple.

Well, what I see here is that 12,22 and 11 are whole numbers, then why is this not a simple ratio?
The ratio of C, H and O atoms of 12:22:11 is likely to be sucrose. Glucose has a simpler ratio of 1:2:1 (even though it has 6 carbons). The usual context for presenting the theory is with inorganic compounds with no more than a 2:3 or 3:5 ratio. With this limitation, they use the words simple ratio since the numbers are small and can easily be found. The ratio of 12:22:11 could be confused with another ratio if your calculations are off by 20%.