Average and Profits and Percentages

Question

The average monthly income of person in a certain family of $5$ is Rs. $1000$. What will be monthly average income of person in the same family if the income of one person increased by Rs. $12000$ per year?

Answer 1

You have 5 incomes, say $x_1, \ldots, x_5$ and $$1000 = \bar{x} = \frac{x_1 + \ldots + x_5}{5}.$$

Now you are saying one of the incomes grew by 12000. Then, the new average income is given by $$ \frac{x_1 + \ldots + x_5 + 12000}{5} $$ Can you tell by how much the average income has increased now?