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The question asks: If $ 12\frac{1}{2}\% $ of a sum of money is $40, what is the total sum of money?

We can break this down step by step:

1. $ 12\frac{1}{2}\% $ can be written as a decimal:
   \[
   12\frac{1}{2}\% = \frac{25}{2}\% = \frac{25}{200} = 0.125
   \]
   
2. The question tells us that $ 0.125 \times \text{Total sum} = 40 $.

3. To find the total sum, we divide $40 by 0.125:
   \[
   \text{Total sum} = \frac{40}{0.125} = 320
   \]

Thus, the total sum of money is **$320**. The correct answer is **(B) $320**.

Would you like more details or have any questions? Here are some related questions you might explore:

1. How would the total sum change if $ 15\% $ of the sum was given instead of $ 12\frac{1}{2}\% $?
2. How can you convert percentages with fractions into decimals more efficiently?
3. What is the relationship between percentages and fractions?
4. How can we set up equations to solve real-world problems involving percentages?
5. What other types of financial problems involve percentages?

**Tip:** When converting a percentage to a decimal, divide the percentage by 100. For example, $ 12.5\% $ becomes 0.125.

If 12 1/2 % of a sum of money is $40, what is the total sum of money?

This problem explains how to calculate the total sum of money when 12 1/2 % equals $40. It covers percentage and algebraic concepts for students in Grades 6-8.

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