The ratio of Tianwei's height to Bala's height is 6 : 5.
Bala is $\frac{10}{11}$ as tall as Chelsea. What is the ratio of Tianwei's height to Chelsea's height?

1. Express the relationship between Bala and Chelsea as a ratio

Since Bala is $\frac{10}{11}$ as tall as Chelsea, the ratio of Bala's height to Chelsea's height is $10 : 11$.

2. Find a common multiple for Bala's units in both ratios

Tianwei : Bala = $6 : 5$
Bala : Chelsea = $10 : 11$
To combine the ratios, make Bala's units the same. The lowest common multiple of $5$ and $10$ is $10$.
Multiply the first ratio by $2$:
Tianwei : Bala = $12 : 10$

3. Determine the ratio of Tianwei's height to Chelsea's height

Tianwei : Bala : Chelsea = $12 : 10 : 11$
Therefore, Tianwei : Chelsea = $12 : 11$.