Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?

Options

A. A) 10 : 5
B. B) 15 : 2
C. C) 20 : 2
D. D) 25 : 2

Answer

To solve the problem, we need to find the ratio of US stamps to British stamps based on the given ratios of US to Indian stamps and Indian to British stamps.

### Step-by-Step Solution:

1. **Identify the given ratios**:
- The ratio of US to Indian stamps is given as \(5:2\).
- The ratio of Indian to British stamps is given as \(5:1\).

2. **Express the ratios in terms of variables**:
- Let the number of US stamps be \(5x\).
- Let the number of Indian stamps be \(2x\).
- Let the number of British stamps be \(y\).

3. **Set up the second ratio**:
- From the ratio of Indian to British stamps \(5:1\), we can express the number of British stamps in terms of Indian stamps:
\[ \frac{2x}{y} = \frac{5}{1} \implies y = \frac{2x}{5} \]

4. **Find a common term for British stamps**:
- To express the British stamps in terms of \(x\), we can say:
\[ y = \frac{2x}{5} \]
- To make calculations easier, we can multiply both sides of this equation by 5 to eliminate the fraction:
\[ 5y = 2x \implies y = \frac{2x}{5} \]

5. **Now express the ratio of US to British stamps**:
- We have:
- US stamps = \(5x\)
- British stamps = \(y = \frac{2x}{5}\)
- The ratio of US to British stamps can now be calculated as:
\[ \text{Ratio of US to British} = \frac{5x}{\frac{2x}{5}} = 5x \times \frac{5}{2x} = \frac{25}{2} \]

6. **Final ratio**:
- Therefore, the ratio of US to British stamps is:
\[ 25:2 \]

### Conclusion:
The ratio of US to British stamps is \(25:2\).