In a technology firm, the average monthly earning of a group comprising 6 software engineers and 1 project supervisor is ₹18,000. Provided that the project supervisor earns ₹30,000 per month, calculate the mean monthly earning of the 6 software engineers.

The correct option is ₹16,000.

Step-by-step Explanation:

Step 1: Understand the group composition and given values
The total group consists of 6 software engineers and 1 project supervisor, making a total of:
6 + 1 = 7 people.

The average monthly earning of these 7 people is ₹18,000.
The monthly earning of the project supervisor is ₹30,000.

Step 2: Calculate the total monthly earnings of all 7 people
Using the formula for total sum based on average:

$\text{Total Earnings}=\text{Average Earning}\times \text{Total Number of People}$

$\text{Total Earnings of 7 people}=18000\times 7=₹\mathrm{1,26,000}$

Step 3: Calculate the total monthly earnings of the 6 software engineers
To find the total earnings of only the 6 software engineers, subtract the project supervisor's salary from the total earnings of all 7 people:

$\text{Earnings of 6 Engineers}=\text{Total Earnings of 7 people}-\text{Supervisor's Earning}$

$\text{Earnings of 6 Engineers}=\mathrm{1,26,000}-\mathrm{30,000}=₹\mathrm{96,000}$

Step 4: Calculate the mean monthly earning of the 6 software engineers
Now, divide the total earnings of the 6 engineers by the number of engineers (6):

$\text{Mean Monthly Earning}=\frac{\mathrm{96,000}}{6}=₹\mathrm{16,000}$

Thus, the mean monthly earning of the 6 software engineers is ₹16,000.