# 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 |

Principal | : | Amount | ||

1st year | → | : | ||

2nd year | → | : | ||

Ratio | → | : |

**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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