In how many years will Rs. 2000 amounts to Rs. 2420 at 10% per annum compound interest?

$$\eqalign{ & {\text{Principal = Rs. 2000}} \cr & {\text{Amount = Rs. 2420}} \cr & {\text{Rate = 10% }} \cr & {\text{By using formula,}} \cr & \Rightarrow 2420 = 2000{\left( {1 + \frac{{10}}{{100}}} \right)^n} \cr & \Rightarrow \frac{{2420}}{{2000}} = {\left( {1 + \frac{{10}}{{100}}} \right)^n} \cr & \Rightarrow \frac{{121}}{{100}} = {\left( {\frac{{11}}{{10}}} \right)^n} \cr & \Rightarrow {\left( {\frac{{11}}{{10}}} \right)^2} = {\left( {\frac{{11}}{{10}}} \right)^n} \cr & \Rightarrow n = 2 \cr & {\text{Hence,}} \cr & {\text{required time = 2 years}} \cr} $$

Alternative
Note : In such type of questions to save your valuable time follow the given below method.

		Principal	:	Amount
Ratio	→	2000	:	2420
		100	:	121

$${\text{Rate = 10% = }}\frac{1}{{10}}$$

		Principal	:	Amount
1st year	→	10	:	11
2nd year	→	10	:	11
Ratio	→	100	:	121

Note : Now after 2nd year both the principal and amount will be in the same ratio.
Hence required time = 2 years