Question

In a city, the total income of all people with salary below Rs. 10000 per annum is less than the than the total income of all people with salary abvove Rs. 10000 per annum. If the salaries of people in the first group decrease by 5% and the salaries of people in the second group decrease by 5% then the average income of all people

• A. Increases
• B. Decreases
• C. Remains the same
• D. Cannot be determined from the data.

Answer 1

The correct option is B Decreases

Let the number of person with salary below Rs.$10000$ be $x$ and their salary be A

Then total income $=xA$

the number of person with salary above Rs.$10000$ be $y$ and their salary be $B$

Then total income $=yB$

$xB>xA$ (given)

Average income $=\frac{xA+yB}{x+y}$

When salary of both gropus is decreased by $5\%$

Average income $=\frac{(xA-\frac{5xA}{100})+(yY-\frac{5yB}{100})}{x+y}$

Cleary the average income is less in the second case

So, option $B$ is correct.