Question

In a city, the total income of all people with salary below $₹10000$ per annum is less than the total income of all people with salary above $₹10000$ per annum. If the salaries of people in the first group increases by $5\%$ and the salaries of people in the second group decreases 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

Answer: (B)

Let total number of people whose salary less than $₹10000$ per annum $=x$ and annual salary of each person $=a$
$\therefore$ Total salary $=ax$ and total number of people whose salary more than $₹10000$ per annum $=y$
and annual salary of each person $=b$ $\therefore$ Total salary $=bx$
When $5\%$ increase of salary of people $x$
i.e. $x(a+5\%$ of $a)=\frac{105ax}{100}$
$\frac{\text{ Average salary after }}{\text{ Average salary before }}=\frac{\frac{105ax}{100}+\frac{95by}{100}}{ax+by}$
$=1+\frac{5}{100}\left(\frac{ax-by}{ax+by}\right)$
$ax-by<0$
$\therefore$ Average salary after be decreases.