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
In which year, the percentage increase in expenditure is maximum as compared to its previous year?
2014
Understanding Company Expenditure Trends
The problem provides data on the expenditure of a company over several years, from 2011 to 2017. We are asked to find the year in which the percentage increase in expenditure was the highest compared to the previous year.
Calculating Percentage Increase in Expenditure
To determine the year with the maximum percentage increase, we need to calculate the percentage change in expenditure for each year starting from 2012, comparing it to the expenditure of the preceding year. The formula for percentage increase is:
\(\text{Percentage Increase} = \frac{\text{(Current Year Expenditure - Previous Year Expenditure)}}{\text{Previous Year Expenditure}} \times 100\)
If the result is negative, it indicates a percentage decrease.
Step-by-Step Calculation for Each Year
Let's calculate the percentage change for each year from 2012 to 2017:
- Year 2012: Compared to 2011. Expenditure in 2011 was 13.8 lakhs, and in 2012 it was 15.4 lakhs.
\(\text{Percentage Change}_{2012} = \frac{(15.4 - 13.8)}{13.8} \times 100 = \frac{1.6}{13.8} \times 100 \approx 11.59\%\)
- Year 2013: Compared to 2012. Expenditure in 2012 was 15.4 lakhs, and in 2013 it was 10.4 lakhs.
\(\text{Percentage Change}_{2013} = \frac{(10.4 - 15.4)}{15.4} \times 100 = \frac{-5.0}{15.4} \times 100 \approx -32.47\%\)
(This is a decrease) - Year 2014: Compared to 2013. Expenditure in 2013 was 10.4 lakhs, and in 2014 it was 13.1 lakhs.
\(\text{Percentage Change}_{2014} = \frac{(13.1 - 10.4)}{10.4} \times 100 = \frac{2.7}{10.4} \times 100 \approx 25.96\%\)
- Year 2015: Compared to 2014. Expenditure in 2014 was 13.1 lakhs, and in 2015 it was 15.8 lakhs.
\(\text{Percentage Change}_{2015} = \frac{(15.8 - 13.1)}{13.1} \times 100 = \frac{2.7}{13.1} \times 100 \approx 20.61\%\)
- Year 2016: Compared to 2015. Expenditure in 2015 was 15.8 lakhs, and in 2016 it was 17.2 lakhs.
\(\text{Percentage Change}_{2016} = \frac{(17.2 - 15.8)}{15.8} \times 100 = \frac{1.4}{15.8} \times 100 \approx 8.86\%\)
- Year 2017: Compared to 2016. Expenditure in 2016 was 17.2 lakhs, and in 2017 it was 19.4 lakhs.
\(\text{Percentage Change}_{2017} = \frac{(19.4 - 17.2)}{17.2} \times 100 = \frac{2.2}{17.2} \times 100 \approx 12.79\%\)
We can summarize these calculations in a table:
| Year | Expenditure (lakhs) | Previous Year Expenditure (lakhs) | Change (lakhs) | Percentage Change (%) |
|---|---|---|---|---|
| 2011 | 13.8 | - | - | - |
| 2012 | 15.4 | 13.8 | +1.6 | \(\approx 11.59\%\) |
| 2013 | 10.4 | 15.4 | -5.0 | \(\approx -32.47\%\) |
| 2014 | 13.1 | 10.4 | +2.7 | \(\approx 25.96\%\) |
| 2015 | 15.8 | 13.1 | +2.7 | \(\approx 20.61\%\) |
| 2016 | 17.2 | 15.8 | +1.4 | \(\approx 8.86\%\) |
| 2017 | 19.4 | 17.2 | +2.2 | \(\approx 12.79\%\) |
Identifying the Maximum Percentage Increase
Comparing the percentage changes for the years with an increase:
- 2012: \(\approx 11.59\%\)
- 2014: \(\approx 25.96\%\)
- 2015: \(\approx 20.61\%\)
- 2016: \(\approx 8.86\%\)
- 2017: \(\approx 12.79\%\)
The maximum positive percentage increase is approximately 25.96%, which occurred in the year 2014.
Conclusion
Based on the calculations, the year with the maximum percentage increase in expenditure compared to its previous year is 2014.
Revision Table: Expenditure Data Analysis
Review the key calculations performed to find the maximum percentage increase in company expenditure.
| Year | Previous Year | Percentage Change in Expenditure (%) |
|---|---|---|
| 2012 | 2011 | \(\approx 11.59\%\) |
| 2013 | 2012 | \(\approx -32.47\%\) (Decrease) |
| 2014 | 2013 | \(\approx 25.96\%\) (Maximum Increase) |
| 2015 | 2014 | \(\approx 20.61\%\) |
| 2016 | 2015 | \(\approx 8.86\%\) |
| 2017 | 2016 | \(\approx 12.79\%\) |
Additional Information: Percentage Change Concepts
Percentage change is a fundamental concept used to compare values over time or across different categories. It quantifies the relative change between an initial value and a final value.
- Positive Percentage Change: Indicates an increase. The final value is greater than the initial value.
- Negative Percentage Change: Indicates a decrease. The final value is less than the initial value.
- Base for Calculation: The percentage change is always calculated with respect to the initial value (the previous year's expenditure in this case).
- Applications: Percentage change is widely used in economics (inflation rates, GDP growth), finance (stock price changes, investment returns), and data analysis to understand trends and compare performance.
Understanding percentage change is crucial for interpreting data and identifying periods of significant growth or decline, as demonstrated in the company expenditure analysis.
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