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
The ratio of percentage drop in total production in 2004 compared to 2001 to that in 2000 compared to 2001, is
The question asks us to find the ratio between the percentage drop in total multivitamin tablet production in the year 2004 compared to 2001, and the percentage drop in total production in the year 2000 compared to 2001. We need to use the provided data table which shows the production (in lakhs) of five different types of multivitamin tablets for the years 2000 to 2005.
Calculating Total Production for Relevant Years
First, we need to calculate the total production for the years 2000, 2001, and 2004 by summing the production of all five types of tablets for each of these years.
- Total Production in 2000 = Production(Type 1) + Production(Type 2) + Production(Type 3) + Production(Type 4) + Production(Type 5) \[ \text{Total Production}_{2000} = 160 + 80 + 70 + 90 + 75 = 475 \text{ lakhs} \]
- Total Production in 2001 = Production(Type 1) + Production(Type 2) + Production(Type 3) + Production(Type 4) + Production(Type 5) \[ \text{Total Production}_{2001} = 200 + 150 + 85 + 160 + 100 = 695 \text{ lakhs} \]
- Total Production in 2004 = Production(Type 1) + Production(Type 2) + Production(Type 3) + Production(Type 4) + Production(Type 5) \[ \text{Total Production}_{2004} = 180 + 110 + 85 + 95 + 115 = 585 \text{ lakhs} \]
Here is a summary table for the total production:
| Year | Total Production (in lakhs) |
|---|---|
| 2000 | 475 |
| 2001 | 695 |
| 2004 | 585 |
Calculating Percentage Drop in 2004 Compared to 2001
Next, we calculate the percentage drop in total production in 2004 relative to 2001. A percentage drop is calculated using the formula:
\[ \text{Percentage Drop} = \left( \frac{\text{Value in Base Year} - \text{Value in Comparison Year}}{\text{Value in Base Year}} \right) \times 100 \]In this case, the base year is 2001 and the comparison year is 2004.
- Drop in Production = Total Production\(_{2001}\) - Total Production\(_{2004}\) \[ \text{Drop} = 695 - 585 = 110 \text{ lakhs} \]
- Percentage Drop (2004 vs 2001) = \( \left( \frac{110}{695} \right) \times 100 \)
Calculating Percentage Drop in 2000 Compared to 2001
Now, we calculate the percentage drop in total production in 2000 relative to 2001. Here, the base year is 2001 and the comparison year is 2000.
- Drop in Production = Total Production\(_{2001}\) - Total Production\(_{2000}\) \[ \text{Drop} = 695 - 475 = 220 \text{ lakhs} \]
- Percentage Drop (2000 vs 2001) = \( \left( \frac{220}{695} \right) \times 100 \)
Determining the Ratio of Percentage Drops
Finally, we need to find the ratio of the percentage drop calculated in the previous steps.
Ratio = \( \frac{\text{Percentage Drop (2004 vs 2001)}}{\text{Percentage Drop (2000 vs 2001)}} \)
Substituting the values we calculated:
\[ \text{Ratio} = \frac{\left( \frac{110}{695} \right) \times 100}{\left( \frac{220}{695} \right) \times 100} \]The \( \times 100 \) and the denominator \( 695 \) cancel out:
\[ \text{Ratio} = \frac{110}{220} \]Simplifying the fraction:
\[ \text{Ratio} = \frac{1}{2} \]Thus, the ratio of the percentage drop in total production in 2004 compared to 2001 to that in 2000 compared to 2001 is \( \frac{1}{2} \). This corresponds to Option 3.
Similar Questions
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Year 2015
Year 2016
Country A
35
38
Country B
45
47
Country C
88
93
Country D
75
79
Country E
58
60.9
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Number of
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5
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8
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12
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