Raju invested $\text{Rs. }15,000$ in two parts. One part at $8\%$ and the other at $12\%$ per annum. His total annual income from interest is $\text{Rs. }1640$. The ratio of the two parts respectively is:

Let the part invested at $8\%$ be $\text{Rs. }x$ and the part invested at $12\%$ be $\text{Rs. }(15000-x)$.
The total annual income is the sum of simple interest from both parts:

$$\frac{x\times 8\times 1}{100}+\frac{(15000-x)\times 12\times 1}{100}=1640$$

$$8x+12(15000-x)=1640\times 100$$

$$8x+180000-12x=164000$$

$$-4x=164000-180000$$

$$-4x=-16000$$

$$x=4000$$

So, the first part is $\text{Rs. }4000$.
The second part is:

$$15000-4000=\text{Rs. }11000$$

The ratio of the two parts is:

$$\frac{4000}{11000}=\frac{4}{11}=4:11$$