Q23 / 59 · KVPY 2013 (SA) · Mathematics

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

  • A
    increases
  • Correct answer
    B
    decreases
  • C
    remains the same
  • D
    cannot be determined from the data

Solution

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. $\mathrm{xA}-\mathrm{yB} < 0$ $\frac{\text { average after }}{\text { average before }}=\frac{x\left(\frac{105}{100} A\right)+y\left(\frac{95}{100} B\right)}{x A+y B}$ $=1+\frac{5}{100}\left(\frac{x A-y B}{x A+y B}\right)$

Hence, the correct answer is option: 'B'.

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