The results of a random survey showed that 22 out of 75 people are suffering from viral fever . Which is the best prediction of the total number of people suffering from fever, if there are 3000 people in a village ?

Options

A. 2500
B. 500
C. 900
D. 2000

Answer

To solve the problem, we need to determine the number of people suffering from viral fever in a village of 3000 people based on the survey results. Here’s a step-by-step solution:

### Step 1: Determine the ratio of people suffering from fever
From the survey, we know that:
- Number of people suffering from fever = 22
- Total number of people surveyed = 75

So, the ratio of people suffering from fever is:
\[ \text{Ratio} = \frac{22}{75} \]

### Step 2: Set up the proportion for the village
We want to find out how many people in a village of 3000 are likely to be suffering from fever. We can set up the proportion as follows:
\[ \frac{22}{75} = \frac{x}{3000} \]
where \( x \) is the number of people suffering from fever in the village.

### Step 3: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:
\[ 22 \times 3000 = 75 \times x \]
This simplifies to:
\[ 66000 = 75x \]

### Step 4: Solve for \( x \)
Now, we divide both sides by 75 to find \( x \):
\[ x = \frac{66000}{75} \]

### Step 5: Calculate \( x \)
Now, we perform the division:
\[ x = 880 \]

### Conclusion
Therefore, the best prediction of the total number of people suffering from fever in the village of 3000 people is **880**.

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