The ratio of the number of Chinese pupils to Malay pupils in a school is 3:7. The ratio of the number of Indian pupils to Malay pupils is 6:17. Find the ratio of the number of Chinese pupils to Indian pupils in the school.

To solve the problem of finding the ratio of Chinese pupils to Indian pupils in the school, we are given the following two ratios:

1. The ratio of Chinese pupils to Malay pupils is 3:7.
2. The ratio of Indian pupils to Malay pupils is 6:17.

Let:
- \( C \) represent the number of Chinese pupils.
- \( M \) represent the number of Malay pupils.
- \( I \) represent the number of Indian pupils.

From the given ratios:
- \( \frac{C}{M} = \frac{3}{7} \), meaning \( C = \frac{3}{7}M \).
- \( \frac{I}{M} = \frac{6}{17} \), meaning \( I = \frac{6}{17}M \).

Now, we want to find the ratio \( \frac{C}{I} \) (the ratio of Chinese pupils to Indian pupils).

Using the expressions for \( C \) and \( I \):

\[
\frac{C}{I} = \frac{\frac{3}{7}M}{\frac{6}{17}M}
\]

Since \( M \) is common in both the numerator and denominator, it cancels out:

\[
\frac{C}{I} = \frac{3}{7} \times \frac{17}{6}
\]

Now, simplify the fraction:

\[
\frac{C}{I} = \frac{3 \times 17}{7 \times 6} = \frac{51}{42}
\]

Finally, simplify \( \frac{51}{42} \) by dividing both the numerator and denominator by their greatest common divisor, which is 3:

\[
\frac{51}{42} = \frac{17}{14}
\]

Therefore, the ratio of Chinese pupils to Indian pupils is \( \boxed{17:14} \).

Would you like further clarification or details? Here are some related questions for further practice:

1. If the total number of Malay pupils is 119, how many Chinese and Indian pupils are there?
2. How would the ratios change if the number of Malay pupils doubled?
3. What is the combined ratio of Chinese, Malay, and Indian pupils?
4. If the total number of pupils in the school is 340, how many pupils belong to each ethnic group?
5. How can you calculate the total number of pupils given only the ratios and the total number of one group?

**Tip:** When working with ratios, multiplying or dividing both parts of the ratio by the same number does not change the relationship.

Solve the problem of finding the ratio of Chinese pupils to Indian pupils using the given ratios: Chinese to Malay pupils (3:7) and Indian to Malay pupils (6:17). This solution demonstrates key mathematical concepts such as ratios, proportions, and fraction simplification, ideal for students in Grades 7-9.

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