The table below presents the percentage profit earned by two companies A and B during the period 2013 to 2018. Based on the data given in the table, answer five questions that follow Yearwise percentage (%) profit [Where profit % = $\frac{Income − Expenditure}{Expenditure} × 100]$Year % Profit Earned A B 2013 20 % 35 % 2014 32 % 30 % 2015 40 % 50 % 2016 25 % 40 % 2017 30 % 30 % 2018 15 % 40 %
In which year is the ratio of income to expenditure of company A the maximum?
2015
To determine the year in which the ratio of income to expenditure of company A is the maximum, we need to understand the relationship between income, expenditure, and profit percentage. The profit percentage of a company is given by the formula:
\(\text{Profit \%} = \left(\frac{\text{Income} - \text{Expenditure}}{\text{Expenditure}}\right) \times 100\)
From the formula, we can derive the ratio of income to expenditure as follows:
\(\frac{\text{Income}}{\text{Expenditure}} = 1 + \frac{\text{Profit \%}}{100}\)
We'll now calculate this ratio for each year based on the profit percentage given for company A:
- For 2013: \(\frac{\text{Income}}{\text{Expenditure}} = 1 + \frac{20}{100} = 1.20\)
- For 2014: \(\frac{\text{Income}}{\text{Expenditure}} = 1 + \frac{32}{100} = 1.32\)
- For 2015: \(\frac{\text{Income}}{\text{Expenditure}} = 1 + \frac{40}{100} = 1.40\)
- For 2016: \(\frac{\text{Income}}{\text{Expenditure}} = 1 + \frac{25}{100} = 1.25\)
- For 2017: \(\frac{\text{Income}}{\text{Expenditure}} = 1 + \frac{30}{100} = 1.30\)
- For 2018: \(\frac{\text{Income}}{\text{Expenditure}} = 1 + \frac{15}{100} = 1.15\)
By comparing these calculated ratios, we see that the highest ratio of income to expenditure occurs in 2015, where the ratio is 1.40.
Thus, the year in which the ratio of income to expenditure of company A is the maximum is 2015.
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