6 `1/4` % of 1600 + 12 `1/2` % of 800 equals

Options

A. 100
B. 200
C. 300
D. 400

Answer

To solve the problem, we need to calculate \(6 \frac{1}{4}\% \) of 1600 and \(12 \frac{1}{2}\% \) of 800, and then add the two results together.

### Step 1: Convert the mixed percentages to improper fractions
1. **Convert \(6 \frac{1}{4}\%\) to an improper fraction:**
\[ 6 \frac{1}{4} = \frac{6 \times 4 + 1}{4} = \frac{24 + 1}{4} = \frac{25}{4} \]
So, \(6 \frac{1}{4}\% = \frac{25}{4}\%\).

2. **Convert \(12 \frac{1}{2}\%\) to an improper fraction:**
\[ 12 \frac{1}{2} = \frac{12 \times 2 + 1}{2} = \frac{24 + 1}{2} = \frac{25}{2} \]
So, \(12 \frac{1}{2}\% = \frac{25}{2}\%\).

### Step 2: Calculate \(6 \frac{1}{4}\% \) of 1600
1. **Calculate \( \frac{25}{4}\% \) of 1600:**
\[ \frac{25}{4}\% \text{ of } 1600 = \frac{25}{4} \times \frac{1600}{100} \]
Simplifying this:
\[ = \frac{25 \times 1600}{4 \times 100} = \frac{40000}{400} = 100 \]

### Step 3: Calculate \(12 \frac{1}{2}\% \) of 800
1. **Calculate \( \frac{25}{2}\% \) of 800:**
\[ \frac{25}{2}\% \text{ of } 800 = \frac{25}{2} \times \frac{800}{100} \]
Simplifying this:
\[ = \frac{25 \times 800}{2 \times 100} = \frac{20000}{200} = 100 \]

### Step 4: Add the two results
1. **Add the results from Step 2 and Step 3:**
\[ 100 + 100 = 200 \]

### Final Answer
Thus, \(6 \frac{1}{4}\% \) of 1600 plus \(12 \frac{1}{2}\% \) of 800 equals **200**.

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