The population of country is 10 crores at present and is expected to grow to 17.28 crores in the next three years. Neglecting the death rate, the uniform annual percentage rate of growth is:

The correct answer is 20.

Step-by-step Explanation:

Let the present population be $P_0$, the population after $n$ years be $P_n$, and the annual percentage rate of growth be $r\%$.

From the given problem, we have:

Present population ($P_0$) = 10 crores

Population after 3 years ($P_3$) = 17.28 crores

Time period ($n$) = 3 years

The formula for population growth compounded annually is given by:

$P_n=P_0{(1+\frac{r}{100})}^n$

Substitute the given values into the formula:

$17.28=10{(1+\frac{r}{100})}^3$

Divide both sides by 10:

$\frac{17.28}{10}={(1+\frac{r}{100})}^3$

$1.728={(1+\frac{r}{100})}^3$

Now, take the cube root of both sides. Since ${1.2}^3=1.728$:

$1.2=1+\frac{r}{100}$

Subtract 1 from both sides:

$0.2=\frac{r}{100}$

Multiply by 100 to solve for $r$:

$r=0.2\times 100=20$

Thus, the uniform annual percentage rate of growth is 20%.