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Question: Answered & Verified by Expert
In a city, the total income of all people with salary below $Rs. 10000$ per annum is less than the total income of all people with salary above $Rs. 10000$ 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
MathematicsStatisticsKVPYKVPY 2013 (SA)
Options:
  • A increases
  • B decreases
  • C remains the same
  • D cannot be determined from the data
Solution:
1212 Upvotes Verified Answer
The correct answer is: decreases
Let total number of people with salary below $\mathrm{Rs. 10000}$ per annum is $x$ and salary is $A$. Let total number of people with salary above $\mathrm{Rs. 10000}$ per annum is $y$ and salary is $B$ then.
$\mathrm{xA}-\mathrm{yB} < 0$
$\frac{\text { average after }}{\text { average before }}=\frac{x\left(\frac{105}{100} A\right)+y\left(\frac{95}{100} B\right)}{x A+y B}$
$=1+\frac{5}{100}\left(\frac{x A-y B}{x A+y B}\right)$

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