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The population of a town first decreased by 16% due to migration to a big city for better job opportunities. The next year, the population of the town
Question

The population of a town first decreased by 16% due to migration to a big city for better job opportunities. The next year, the population of the town increased by 21% as there were better facilities for jobs. What is the net percentage change (correct to 2 decimal places) in the population?

A.

Decrease by 2.54%

B.

Increase by 2.54%

C.

Increase by 1.64%

D.

Decrease by 1.64%

Correct option is C

Given:
Population decrease due to migration = 16%
Population increase thereafter =21%
Formula Used:
Successive increment or decrement of x% and y% are given then
Effective change = x+y+xy100 x + y +\frac{ xy}{100}​​
Solution:
Taking -16% and 21% percent
=16+21+(16×21)100 =1.64= -16+21 +\frac{(-16\times21)}{100} \\\ \\= 1.64%​​
Alternate Method:
For Effective change
=100×((100x))100×((100+y))100 =100×84100×121100=101.64=100 \times \frac{((100-x))}{100}\times \frac{((100+y))}{100} \\\ \\= 100 \times \frac{84}{100} \times \frac{121}{100}= 101.64 

= 1.64%

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