Jo has a collection of US, Indian and British stamps. The ratio of US to Indian stamps is 5 : 2 and the ratio of Indian to British stamps is 5 : 1. What is the ratio of US stamps to British stamps in the collection?

Introduction / Context:
This question involves chaining together two given ratios to find a third related ratio. It is a standard type of ratio and proportion problem where we must express all quantities using a common middle term to avoid confusion.

Given Data / Assumptions:

• Ratio of US to Indian stamps = 5 : 2
• Ratio of Indian to British stamps = 5 : 1
• We need the ratio of US to British stamps.

Concept / Approach:
When two ratios share a common term, we can convert them to equivalent ratios where the common term has the same value in both ratios. Then, we can link them to find the required ratio. Here, Indian stamps are the common middle term, so we will make the Indian part equal in both ratios by appropriate multiplication and then read off the US to British relationship.

Step-by-Step Solution:
Step 1: Let US : Indian = 5 : 2. Step 2: Let Indian : British = 5 : 1. Step 3: To connect these, we want the Indian term in both ratios to be equal. Step 4: The first ratio has Indian = 2 parts, the second has Indian = 5 parts. Step 5: Make them equal by a common multiple. Multiply the first ratio by 5 to get US : Indian = 25 : 10. Step 6: Multiply the second ratio by 2 to get Indian : British = 10 : 2. Step 7: Now Indian = 10 in both, so US : British = 25 : 2.

Verification / Alternative check:
We can assume a concrete number of Indian stamps, say 10. Then US stamps would be (5 / 2) * 10 = 25 and British stamps would be (1 / 5) * 10 * 5? A simpler way: from the combined ratios we already have US = 25, Indian = 10 and British = 2. The ratio US : British is 25 : 2, which matches the derived expression.

Why Other Options Are Wrong:
Ratios like 10 : 5, 15 : 2 or 20 : 2 come from multiplying only one of the given ratios or from not aligning the Indian term correctly in both ratios. They do not preserve the given relationships simultaneously. Only 25 : 2 is consistent with both original ratios when the Indian term is matched.

Common Pitfalls:
Students sometimes add or subtract ratios or try to combine them without equalizing the common term. Another mistake is to equate 2 directly with 5 without using a common multiple, which leads to incorrect scaling. Always bring the shared middle term to a common value in both ratios before reading off the desired ratio.

Final Answer:
The ratio of US to British stamps is 25 : 2.