Study the following graphs which show the number of workers of different categories of a factory for two different years. The total number of workers in 1998 was 2000, and in 2000 was 2400.
Question: 1
In which of the categories is the number of workers same in both the years?
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When comparing two years for the same category, check the percentages for both years and see if they match.
By comparing the two pie charts for the years 1998 and 2000, we find that the number of workers in category S remains unchanged across both years. The percentage of workers in category S is the same in both 1998 and 2000, indicating that the number of workers in this category did not vary.
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Question: 2
Find the percentage increase in the number of workers in category U in 2000:
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To calculate percentage increase, use the formula \( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100 \).
In 1998, the number of workers in category U was 8% of 2000, which equals 160 workers. In 2000, the number of workers in category U was 10% of 2400, which equals 240 workers. The percentage increase in the number of workers is calculated as follows:
\[
\text{Percentage increase} = \frac{240 - 160}{160} \times 100 = 50%
\]
Thus, the number of workers in category U increased by 50% from 1998 to 2000.
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Question: 3
What is the total number of increased workers for the categories in which the number of workers has been increased?
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For total increase, sum the difference in workers for each category where the number increased.
From the graphs, we observe that the categories with an increase in the number of workers are U, T, and P. To find the total number of increased workers, we need to sum the increase in the number of workers for each of these categories.
For each category:
- Category U: Increase of 80 workers
- Category T: Increase of 120 workers
- Category P: Increase of 208 workers
Summing the increases:
\[
\text{Total increase} = 80 + 120 + 208 = 408
\]
Thus, the total number of increased workers for these categories is 408.
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Question: 4
Which categories have shown a decrease in the number of workers from 1998 to 2000?
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To identify categories with a decrease, look for categories where the percentage in 2000 is less than in 1998.
By examining the graphs for 1998 and 2000, we can see that the categories P and Q have witnessed a decrease in the number of workers. In 2000, both categories show a lower percentage of workers compared to 1998, indicating a reduction in the number of workers for these categories.
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Question: 5
Find the maximum difference between the number of workers of any two categories taken together for any one year and that of any two for the other year.
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To calculate the maximum difference, find the sum of workers in two categories and subtract the lesser from the greater value.
To find the maximum difference between the number of workers in two categories for the two different years, we need to compare the sum of workers in two categories from both years. After analyzing the graphs, the largest difference is observed between categories T and Q in 1998 (with a combined total of 660 workers) and between categories T and R in 2000 (also showing a difference of 660 workers).
Thus, the maximum difference is 660 workers.
