Question

The population of a city increase at the rate of $4\%$ per annum. there is additional annual increase of $1\%$ due to influx of job seeker. The $\%$ increase in the population after $2$ years is

• A. $10$
• B. $10.25$
• C. $10.5$
• D. $10.75$

Answer 1

Answer: (B)

$10.25$

Final population $=$ initial population ${(1+\frac{rate}{100})}^{time}.$

Let the initial population $=x$.

The rate $=(4+1)\%$ p.a.

Time $=2$ yrs

$\therefore$ the population after $2$ yrs. $=$ $x\times {(1+\frac{5}{100})}^2=\frac{441x}{400}.$

$\therefore$ the rise in population $=$ $\frac{441x}{400}-x$

$=\frac{41x}{400}$

$=\frac{41x}{400}\times 100$ p.c

$=10.25\%$