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:

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.