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