Many starts from a place A and reaches the place B in 29 hours. He travels 219 distance at the speed of 9 km/hr and the remaining distance at the speed of 12 km/hr. What is the distance between A and B?

Let the total distance between the two places be $$D \text{ km}$$.

According to the question, the traveller covers $$\frac{2}{9}$$ of this distance at a speed of $$9 \text{ km h}^{-1}$$ and the remaining $$\left(1-\frac{2}{9}\right)=\frac{7}{9}$$ of the distance at a speed of $$12 \text{ km h}^{-1}$$. The total time taken is $$29 \text{ h}$$.

Time taken to cover the first part:
$$\text{Time}_1=\frac{\dfrac{2}{9}D}{9}= \frac{2D}{81}\ \text{h}$$

Time taken to cover the remaining part:
$$\text{Time}_2=\frac{\dfrac{7}{9}D}{12}= \frac{7D}{108}\ \text{h}$$

Total time condition:
$$\frac{2D}{81}+\frac{7D}{108}=29$$

Bring both fractions to a common denominator $$324$$:
$$\frac{2D}{81}=\frac{8D}{324},\quad \frac{7D}{108}=\frac{21D}{324}$$
Hence
$$\frac{8D}{324}+\frac{21D}{324}=29$$

Simplify the left-hand side:
$$\frac{29D}{324}=29$$

Multiply both sides by $$324$$:
$$29D = 29 \times 324$$

Divide by $$29$$:
$$D = 324 \text{ km}$$

Therefore, the distance between places A and B is $$324\ \text{km}$$.

Option C which is: 324 km