Four examiners can examine a certain number of answer
papers in 10 days by working for 5 hours a day. For how
many hours in a day would 2 examiners have to work in order
to examine twice the number of answer papers in 20 days?

Options

A. 8 hours
B. `7 1/2 `days
C. 10 hours
D. ` 8 1/2` hours

Explanation

To solve the problem, we can use the relationship between the number of examiners, the number of days, and the number of hours they work. The formula we will use is:

\[ M_1 \times D_1 \times H_1 = M_2 \times D_2 \times H_2 \]

Where:
- \( M_1 \) = Number of men (examiners) in the first scenario
- \( D_1 \) = Number of days in the first scenario
- \( H_1 \) = Number of hours worked per day in the first scenario
- \( M_2 \) = Number of men (examiners) in the second scenario
- \( D_2 \) = Number of days in the second scenario
- \( H_2 \) = Number of hours worked per day in the second scenario

### Step 1: Identify the values from the problem
From the problem, we have:
- \( M_1 = 4 \) (four examiners)
- \( D_1 = 10 \) (10 days)
- \( H_1 = 5 \) (5 hours a day)
- \( M_2 = 2 \) (two examiners)
- \( D_2 = 20 \) (20 days)
- We want to find \( H_2 \) (the number of hours per day for the two examiners)

### Step 2: Set up the equation
Using the formula, we can set up the equation as follows:
\[ 4 \times 10 \times 5 = 2 \times 20 \times H_2 \]

### Step 3: Calculate the left side of the equation
Calculating the left side:
\[ 4 \times 10 \times 5 = 200 \]

### Step 4: Substitute and simplify the equation
Now we substitute back into the equation:
\[ 200 = 2 \times 20 \times H_2 \]

### Step 5: Calculate the right side
Calculating the right side:
\[ 2 \times 20 = 40 \]
So now the equation is:
\[ 200 = 40 \times H_2 \]

### Step 6: Solve for \( H_2 \)
To find \( H_2 \), we divide both sides by 40:
\[ H_2 = \frac{200}{40} = 5 \]

### Step 7: Conclusion
Thus, the number of hours in a day that 2 examiners would have to work to examine twice the number of answer papers in 20 days is **5 hours**.

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