Direction: For the next items, consider the following data with regard to different types (1, 2, 3, 4, 5) of multivitamin tablets produced in a company (in lakhs): Year 1 2 3 4 5 2000 160 80 70 90 75 2001 200 150 85 160 100 2002 135 35 44 95 85 2003 240 95 120 80 120 2004 180 110 85 95 115 2005 210 150 100 92 110
In which one of the following pairs of years, the difference in total number of tablets produced between them is minimum?
(2003, 2005)
Finding Minimum Difference in Tablet Production
The question asks us to identify the pair of years from the given options where the difference in the total number of multivitamin tablets produced is the minimum. To solve this, we first need to calculate the total number of tablets produced in each year from 2000 to 2005 by summing up the production of all five types of tablets for that year.
Here is the production data provided:
Year | 1 | 2 | 3 | 4 | 5 |
2000 | 160 | 80 | 70 | 90 | 75 |
2001 | 200 | 150 | 85 | 160 | 100 |
2002 | 135 | 35 | 44 | 95 | 85 |
2003 | 240 | 95 | 120 | 80 | 120 |
2004 | 180 | 110 | 85 | 95 | 115 |
2005 | 210 | 150 | 100 | 92 | 110 |
Calculating Total Tablet Production Per Year
We sum the production figures across all types for each year:
- Year 2000: \(160 + 80 + 70 + 90 + 75 = 475\) lakhs
- Year 2001: \(200 + 150 + 85 + 160 + 100 = 695\) lakhs
- Year 2002: \(135 + 35 + 44 + 95 + 85 = 394\) lakhs
- Year 2003: \(240 + 95 + 120 + 80 + 120 = 655\) lakhs
- Year 2004: \(180 + 110 + 85 + 95 + 115 = 585\) lakhs
- Year 2005: \(210 + 150 + 100 + 92 + 110 = 662\) lakhs
Let's summarize the total production per year:
| Year | Total Production (lakhs) |
| 2000 | 475 |
| 2001 | 695 |
| 2002 | 394 |
| 2003 | 655 |
| 2004 | 585 |
| 2005 | 662 |
Calculating Differences for Given Pairs of Years
Now, we calculate the difference in total production for each pair of years provided in the options. We are looking for the absolute difference.
- Option 1: (2003, 2005)
Difference = \(| \text{Total in 2003} - \text{Total in 2005} | = |655 - 662| = |-7| = 7\) lakhs - Option 2: (2001, 2005)
Difference = \(| \text{Total in 2001} - \text{Total in 2005} | = |695 - 662| = |33| = 33\) lakhs - Option 3: (2003, 2004)
Difference = \(| \text{Total in 2003} - \text{Total in 2004} | = |655 - 585| = |70| = 70\) lakhs - Option 4: (2000, 2002)
Difference = \(| \text{Total in 2000} - \text{Total in 2002} | = |475 - 394| = |81| = 81\) lakhs
Identifying the Minimum Difference
Comparing the differences calculated for each pair:
- (2003, 2005): 7 lakhs
- (2001, 2005): 33 lakhs
- (2003, 2004): 70 lakhs
- (2000, 2002): 81 lakhs
The minimum difference in the total number of tablets produced is 7 lakhs, which occurred between the years 2003 and 2005.
Conclusion
The pair of years with the minimum difference in the total number of tablets produced is (2003, 2005).
Revision Table: Key Steps
| Step | Description | Purpose |
| 1 | Calculate total production for each year. | Find overall production figures per year. |
| 2 | List total production figures. | Organize calculated data. |
| 3 | Calculate the difference between total production for each pair of years in options. | Determine production difference for pairs. |
| 4 | Compare differences. | Find the minimum difference. |
| 5 | Identify the corresponding pair of years. | Answer the question. |
Additional Information: Data Interpretation
Data interpretation questions often require extracting specific information from tables or charts and performing calculations like sums, averages, percentages, ratios, or differences. It is important to read the question carefully to understand exactly what is being asked. When dealing with differences, pay attention to whether the absolute difference or the difference with a specific sign is needed, though in this case, "difference" usually implies the absolute difference in production volume.
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