If 4 examiners can examine a certain number of answer books in 8 days by working 5 hours a day. For how many hours a day would 2 examiners have to work in order to examine twice the number of answer book in 20 days ?

Options

A. 6 hours
B. 8 hours
C. 9 hours
D. 7 1/2 hours

Answer

To solve the problem step by step, we will use the concept of work done, which can be expressed as:

\[ \text{Work} = \text{Number of Examiners} \times \text{Number of Days} \times \text{Hours per Day} \]

### Step 1: Calculate the total work done by the first group of examiners.

Given:
- Number of examiners (m1) = 4
- Number of days (d1) = 8
- Hours per day (h1) = 5

Using the formula for work, we can calculate the total work (W1):

\[ W1 = m1 \times d1 \times h1 = 4 \times 8 \times 5 \]

Calculating this gives:

\[ W1 = 160 \text{ hours of work} \]

### Step 2: Determine the total work required for the second group of examiners.

Since the second group of examiners needs to examine twice the number of answer books, the work (W2) will be:

\[ W2 = 2 \times W1 = 2 \times 160 = 320 \text{ hours of work} \]

### Step 3: Set up the equation for the second group of examiners.

Now we have:
- Number of examiners (m2) = 2
- Number of days (d2) = 20
- Hours per day (h2) = ? (this is what we need to find)

Using the work formula again for the second group:

\[ W2 = m2 \times d2 \times h2 \]

Substituting the known values:

\[ 320 = 2 \times 20 \times h2 \]

### Step 4: Solve for h2.

Now we can simplify the equation:

\[ 320 = 40 \times h2 \]

To find \( h2 \), divide both sides by 40:

\[ h2 = \frac{320}{40} = 8 \text{ hours} \]

### Conclusion

Thus, 2 examiners would have to work **8 hours a day** to examine twice the number of answer books in 20 days.