In a state, the textile industry output in 2020 was ₹10,000 crore and in 2022 it was ₹12,500 crore. What is the compound annual growth rate (CAGR) of the output from 2020 to 2022?

Step-by-step solution

1. Write the CAGR formula: $\mathrm{CAGR}={\left(\frac{V_f}{V_i}\right)}^{\frac{1}{n}}-1$ where $V_i$ is initial value, $V_f$ is final value and $n$ is number of years.
2. Substitute the given values: $V_i=10,000$, $V_f=12,500$, $n=2$.
3. Compute the ratio: $\frac{12,500}{10,000}=1.25$. Compute the square root: $\sqrt{1.25}\approx 1.1180$.
4. Subtract 1 to obtain the growth factor: $1.1180-1=0.1180$. Convert to a percentage: $0.1180\times 100\approx 11.8$.
5. Thus the CAGR is approximately 11.8%.

Concept tested: CAGR calculation for industry growth

Published 7 October 2026 · How this solution was prepared and checked