Question

The population of a town increases 4% annually but is decreased by emigration annually to the extent of \(\frac{1}{2}\) % . What will be the increase per cent in 3 years ? 

(a) 9.8 

(b) 10 

(c) 10.5 

(d) 10.8

Answer 1

(d) 10.8

Net increase in population in a year = \(\big(4-\frac{1}{2}\big)\)% = 3\(\frac{1}{2}\) %

Let the original population of the town be 100. Then,

Population after 3 years = 100\(\big(1+\frac{3.5}{100}\big)^3\)

= \(\frac{100\times207\times 207\times207}{100\times100\times100}\) = 110.87

\(\therefore\) % increase = (110.87 – 100)% = 10.87% = 10.8%