A boy who was asked to find 3 `1/2` % of a sum of money misread the question and found 5 `1/2`% of It. His answer was 220. What would have been the correct answer?

Options

A. 120
B. 140
C. 160
D. 150

Answer

To solve the problem step by step, we need to find out what 3.5% of the sum of money is, given that 5.5% of it equals 220.

### Step 1: Understand the given information
We know that 5.5% of a certain sum of money equals 220.

### Step 2: Set up the equation
Let the sum of money be represented as \( x \). According to the information given:
\[ 5.5\% \text{ of } x = 220 \]
This can be written in equation form as:
\[ \frac{5.5}{100} \times x = 220 \]

### Step 3: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{220 \times 100}{5.5} \]
Now, calculate \( \frac{220 \times 100}{5.5} \).

### Step 4: Simplify the calculation
First, simplify \( \frac{220}{5.5} \):
\[ \frac{220}{5.5} = \frac{2200}{55} = 40 \]
So,
\[ x = 40 \times 100 = 4000 \]

### Step 5: Calculate 3.5% of \( x \)
Now that we have \( x = 4000 \), we need to find 3.5% of this amount:
\[ 3.5\% \text{ of } 4000 = \frac{3.5}{100} \times 4000 \]
Calculating this gives:
\[ = 3.5 \times 40 = 140 \]

### Final Answer
Thus, the correct answer that the boy should have found is:
\[ \boxed{140} \]