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Examveda

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

A. 3 years

B. $$2\frac{1}{2}$$ years

C. 2 years

D. $$1\frac{1}{2}$$ years

Answer: Option C

Solution(By Examveda Team)

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

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

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