Solution:
Given:
- 4 examiners can examine a certain number of answer books in 8 days by working 5 hours a day.
- 2 examiners need to examine twice the number of answer books in 20 days.
Let's assume the certain number of answer books is x.Step 1: Find the total number of hours worked by 4 examiners in 8 days.
Total hours worked = 4 examiners × 8 days × 5 hours per day = 160 hoursStep 2: Find the total number of answer books examined by 4 examiners in 160 hours.
Total answer books examined = xStep 3: Find the rate at which each examiner examines answer books per hour.
Rate of examination per examiner per hour = x / (4 examiners × 160 hours)Step 4: Find the total number of answer books that need to be examined by 2 examiners in 20 days.
Total answer books to be examined = 2 × xStep 5: Find the total number of hours required by 2 examiners to examine 2x answer books.
Total hours required = (2x) / (2 examiners × Rate of examination per examiner per hour)Step 6: Find the number of hours per day required by 2 examiners to examine 2x answer books in 20 days.
Hours per day = Total hours required / (2 examiners × 20 days)Substituting the values:
Hours per day = (2x) / (2 × Rate of examination per examiner per hour × 20 days)
Hours per day = (2x) / (2 × (x / (4 × 160)) × 20)
Hours per day = (2x) / (x / 128)
Hours per day = 256 / xTherefore, 2 examiners would have to work for (256 / x) hours per day to examine twice the number of answer books in 20 days.
