KVPY SA Exam 2013 Question Paper

Question : 15 of 80

Marks: +1, -0

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

increases
decreases
remains the same
cannot be determined from the data

Validate

Solution:

Let total number of people with salary below Rs. 10000 per annum is x and salary is A. Let total number of people with salary above Rs. 10000 per annum is y and salary is B then.
xA - yB < 0

\text"average after"/\text"average before"

={x(105/100\A)+y(95/100\B)}/{x\A+y\B}

=1+5/100({x\A-y\B}/{x\A+y\B})

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