The output of the textile sector in India was 12 lakh tonnes in 2000 and increased to 27 lakh tonnes in 2010. Calculate the Compound Annual Growth Rate (CAGR) of the sector over this period. (Give your answer in % to one decimal place.)

Step-by-step solution

1. Write the CAGR formula: $\text{CAGR}={\left(\frac{\text{Final value}}{\text{Initial value}}\right)}^{\frac{1}{n}}-1$, where $n$ is the number of years.
2. Substitute the given values: $\frac{27}{12}=2.25$ and $n=10$ years.
3. Compute the 10th root: $2.25^{\frac{1}{10}}$.
4. Use logarithms: $\ln (2.25)=0.81093$, divide by 10 gives $0.081093$, exponentiate to get $e^{0.081093}=1.0844$.
5. Subtract 1: $1.0844-1=0.0844$.
6. Convert to percentage: $0.0844\times 100=8.44\%$, round to one decimal place gives $8.4\%$.
7. State the final answer.

Concept tested: Growth rate calculation

Published 30 August 2026 · How this solution was prepared and checked

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