Direction : Consider the following data for the two (02) items that follow: The expenditure (in lakhs of rupees) of a company for the years 2011 to 2017 is as under : Year Expenditure 2011 13.8 2012 15.4 2013 10.4 2014 13.1 2015 15.8 2016 17.2 2017 19.4
How many times the increase in expenditure in a year exceeded by more than 15% as compared to previous year?
2
Understanding Expenditure Increase Trends
This problem requires us to analyze the yearly expenditure data of a company from 2011 to 2017. The main goal is to determine how many times the increase in expenditure from one year to the next was more than 15%.
Company Expenditure Data (2011-2017)
The provided data shows the expenditure in lakhs of rupees:
| Year | Expenditure (in lakhs of rupees) |
|---|---|
| 2011 | 13.8 |
| 2012 | 15.4 |
| 2013 | 10.4 |
| 2014 | 13.1 |
| 2015 | 15.8 |
| 2016 | 17.2 |
| 2017 | 19.4 |
Calculating Percentage Expenditure Increase
To find out when the expenditure increase exceeded 15%, we must calculate the percentage change year over year. The formula for percentage increase is:
Percentage Increase = \(\\LARGE \\frac{\\text{Expenditure in Current Year} - \\text{Expenditure in Previous Year}}{\\text{Expenditure in Previous Year}} \\times 100\)
We will apply this formula for each consecutive year pair and check if the result is greater than 15%.
Step-by-Step Analysis of Expenditure Increase
- 2011 to 2012:
- Expenditure Change: \(15.4 - 13.8 = 1.6\) lakhs.
- Percentage Increase: \(\\left( \\frac{1.6}{13.8} \\right) \\times 100 \\approx 11.59\\%\).
- Comparison: \(11.59\\%\) is not more than 15%.
- 2012 to 2013:
- Expenditure Change: \(10.4 - 15.4 = -5.0\) lakhs.
- Percentage Change: \(\\left( \\frac{-5.0}{15.4} \\right) \\times 100 \\approx -32.47\\%\).
- Comparison: This is a decrease, not an increase exceeding 15%.
- 2013 to 2014:
- Expenditure Change: \(13.1 - 10.4 = 2.7\) lakhs.
- Percentage Increase: \(\\left( \\frac{2.7}{10.4} \\right) \\times 100 \\approx 25.96\\%\).
- Comparison: \(25.96\\%\) exceeds 15%. (Count: 1)
- 2014 to 2015:
- Expenditure Change: \(15.8 - 13.1 = 2.7\) lakhs.
- Percentage Increase: \(\\left( \\frac{2.7}{13.1} \\right) \\times 100 \\approx 20.61\\%\).
- Comparison: \(20.61\\%\) exceeds 15%. (Count: 2)
- 2015 to 2016:
- Expenditure Change: \(17.2 - 15.8 = 1.4\) lakhs.
- Percentage Increase: \(\\left( \\frac{1.4}{15.8} \\right) \\times 100 \\approx 8.86\\%\).
- Comparison: \(8.86\\%\) is not more than 15%.
- 2016 to 2017:
- Expenditure Change: \(19.4 - 17.2 = 2.2\) lakhs.
- Percentage Increase: \(\\left( \\frac{2.2}{17.2} \\right) \\times 100 \\approx 12.79\\%\).
- Comparison: \(12.79\\%\) is not more than 15%.
Final Count of Expenditure Increases Over 15%
After reviewing the calculations for each year:
- The expenditure increase from 2013 to 2014 was approximately 25.96%.
- The expenditure increase from 2014 to 2015 was approximately 20.61%.
These are the only two instances where the percentage increase in expenditure compared to the previous year was more than 15%.
Therefore, the total count is 2.
Similar Questions
Consider the following data with regard to production of cars (In lakhs):
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
In which of the countries, the production of cars has increased by more than or equal to 5% in 2016 over 2015?The following table shows the marks of 90 students in a test of 80 marks:
Marks
Number of
Students
1 – 10
5
11 – 20
8
21 – 30
10
31 – 40
13
41 – 50
18
51 – 60
17
61 – 70
12
71 – 80
7
The percentage of students who have obtained less than or equal to 50% marks isWhat is the total population of the city (in lakhs)?
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