Question

In a public school there is an increase in number of admissions every year. The number of students in 2000 was 780 and it increased to 3000 in the year 2005. Find the annual increase?

• A. 25 %
• B. 31 %
• C. 39 %
• D. 20 %

Answer 1

The correct option is B

31 %

We need to use Compound Annual Growth Rate (CAGR) for this question :
Conventionally, CAGR is computed using the formula $\left[\right(\frac{Final}{Initial}{)}^{\frac{1}{n}}-1]$
Using the reverse gear approach ,we can obtain the answer much faster
$\frac{Final}{Initial}=\frac{3000}{780}\approx 3.8$

We need to look for something close to 3.8 in the answer options
here n = 5.
Choose a middle answer option,assuming the answer is $30\%$

$(1.3{)}^5=(1.3{)}^2\times (1.3{)}^3=17\times 17\times 1.3=\mathrm{3.75.}$
Hence, the answer will be slightly higher than this = $31\%$
Option (b)