The following table shows the Income (in lakh) and percentage (%) profit of a company over the six years from 2017 to 2022. Based on the data in the table, answer the questions that follow.

Year-wise Income and Profit of a Company

Year	Income (in ₹ lakh)	Profit (%)
2017	120	7.5
2018	160	15
2019	130	22.5
2020	170	17.5
2021	190	20
2022	150	27.5

Approximately what was the average expenditure during the year from 2017 to 2022?

The correct option is 130 lakh.

Step-by-Step Explanation:

To find the average expenditure of the company during the years from 2017 to 2022, we first need to calculate the expenditure for each individual year. Let's recall the standard relationship between Income, Expenditure, and Profit percentage (%):

$$\text{Profit (\%)}=\frac{\text{Income}-\text{Expenditure}}{\text{Expenditure}}\times 100$$

Let $I$ represent the Income, $E$ represent the Expenditure, and $P$ represent the Profit percentage. Rearranging the formula to solve for Expenditure ($E$) gives:

$$E=\frac{I}{1+\frac{P}{100}}$$

Now, we apply this formula to calculate the expenditure for each year using the data visible in the table:

1. Year 2017:
Income = 120 lakh, Profit = 7.5%
$$E_{2017}=\frac{120}{1+0.075}=\frac{120}{1.075}\approx 111.63\text{lakh}$$

2. Year 2018:
Income = 160 lakh, Profit = 15%
$$E_{2018}=\frac{160}{1+0.15}=\frac{160}{1.15}\approx 139.13\text{lakh}$$

3. Year 2019:
Income = 130 lakh, Profit = 22.5%
$$E_{2019}=\frac{130}{1+0.225}=\frac{130}{1.225}\approx 106.12\text{lakh}$$

4. Year 2020:
Income = 170 lakh, Profit = 17.5%
$$E_{2020}=\frac{170}{1+0.175}=\frac{170}{1.175}\approx 144.68\text{lakh}$$

5. Year 2021:
Income = 190 lakh, Profit = 20%
$$E_{2021}=\frac{190}{1+0.20}=\frac{190}{1.2}=158.33\text{lakh}$$

6. Year 2022:
Income = 150 lakh, Profit = 27.5%
$$E_{2022}=\frac{150}{1+0.275}=\frac{150}{1.275}\approx 117.65\text{lakh}$$

Step 7: Calculate Total and Average Expenditure
First, sum the expenditures of all six years:
$$\text{Total Expenditure}=111.63+139.13+106.12+144.68+158.33+117.65=777.54\text{lakh}$$

Now, compute the average expenditure by dividing the total expenditure by the number of years (6):
$$\text{Average Expenditure}=\frac{777.54}{6}\approx 129.59\text{lakh}$$

Approximating $129.59$ to the nearest integer option gives 130 lakh.