one hundred and sixty examiners, each marking 100 scripts per day, are needed to mark an examination in 4 weeks. how many days would 250 examiners, each marking 60 scripts in a day, take to mark the same examination?
30 days
160 * 100 * 28 = 250 * 60 * x
Solve for x.
To solve this problem, we need to find the total number of scripts that need to be marked in both cases, and then calculate the number of days required.
Let's start with the first scenario:
- 160 examiners can each mark 100 scripts per day.
- So, in total, they can mark 160 x 100 = 16,000 scripts per day.
- Given that the examination should be completed in 4 weeks, we have 4 x 7 = 28 days.
- Therefore, the total number of scripts that need to be marked is 16,000 x 28 = 448,000 scripts.
Now, let's move to the second scenario:
- We have 250 examiners who can each mark 60 scripts per day.
- So, in total, they can mark 250 x 60 = 15,000 scripts per day.
- To determine the number of days required to mark 448,000 scripts, we divide the total number of scripts by the number of scripts that can be marked per day.
- Therefore, it will take 448,000 / 15,000 = 29.87 days to mark the same examination.
Rounding up, it will take approximately 30 days for 250 examiners, each marking 60 scripts per day, to mark the same examination.
To solve this problem, we need to determine the total number of scripts and the rate at which the examiners are marking scripts.
Let's start with the given information:
Number of examiners: 100
Number of scripts marked per day by each examiner: 100
Number of weeks to mark the examination: 4
To find the total number of scripts, we need to multiply the number of examiners by the number of scripts marked per day by each examiner, and then multiply that by the number of days in a week:
Total number of scripts = Number of examiners x Number of scripts marked per day x Number of days in a week
Total number of scripts = 100 x 100 x 7 (since there are 7 days in a week)
Total number of scripts = 700,000
Now, let's calculate the number of days it would take for 250 examiners to mark 60 scripts per day:
Number of examiners: 250
Number of scripts marked per day by each examiner: 60
To find the number of days, we need to divide the total number of scripts by the number of scripts marked per day:
Number of days = Total number of scripts / (Number of examiners x Number of scripts marked per day)
Number of days = 700,000 / (250 x 60)
Number of days ≈ 46 days
So, it would take approximately 46 days for 250 examiners, each marking 60 scripts per day, to mark the same examination.