A sum of money triples itself in 20 years. The rate of interest is:

1. 20%

2. 10%

3. 5%

4. 15%

Given:

A = 3P

T = 20 years

Let the rate be $r$.

$\because \text{A = S.I. + P}\\[1em] \Rightarrow \text{S.I. = A - P}\\[1em] \Rightarrow \text{S.I. = 3P - P}\\[1em] \Rightarrow \text{S.I. = 2P}$

And we know,

$\text{S.I.} = ₹ \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] \Rightarrow \text{2P} = ₹ \Big(\dfrac{P \times r \times 20}{100}\Big)\\[1em] \Rightarrow 2 \cancel{P} = ₹ \dfrac{\cancel{P} \times r \times 20}{100}\\[1em] \Rightarrow 2 = ₹ \dfrac{r}{5}\\[1em] \Rightarrow r = 2 \times 5\\[1em] \Rightarrow r = 10$

Hence, option 2 is the correct option.