India’s No.1 Educational Platform For UPSC,PSC And All Competitive Exam

Download Our App

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

13 years
22 ¹/₂ years
32 years
41 ¹/₂ years

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Principal  =  Rs 2000 \\ Amount  =  Rs 2420 \\ Rate  =  10% \\ By using formula, \\ \Rightarrow 2420 = 2000 {(1 + \frac{10}{100})}^{n} \\ \Rightarrow \frac{2420}{2000} = {(1 + \frac{10}{100})}^{n} \\ \Rightarrow \frac{121}{100} = {(\frac{11}{10})}^{n} \\ \Rightarrow {(\frac{11}{10})}^{2} = {(\frac{11}{10})}^{n} \\ \Rightarrow n = 2 \\ Hence, \\ required time  =  2 years \end{aligned}

$\eqalign{ & {\text{Principal = Rs 2000}} \cr & {\text{Amount = Rs 2420}} \cr & {\text{Rate = 10% }} \cr & {\text{By using formula,}} \cr & \Rightarrow 2420 = 2000{\left( {1 + \frac{{10}}{{100}}} \right)^n} \cr & \Rightarrow \frac{{2420}}{{2000}} = {\left( {1 + \frac{{10}}{{100}}} \right)^n} \cr & \Rightarrow \frac{{121}}{{100}} = {\left( {\frac{{11}}{{10}}} \right)^n} \cr & \Rightarrow {\left( {\frac{{11}}{{10}}} \right)^2} = {\left( {\frac{{11}}{{10}}} \right)^n} \cr & \Rightarrow n = 2 \cr & {\text{Hence,}} \cr & {\text{required time = 2 years}} \cr}$ Alternative
Note : In such type of questions to save your valuable time follow the given below method.

		Principal	:	Amount
Ratio	→	2000	:	2420
		100	:	121

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

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

		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

Workspace Report

Post your Comments

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

		Principal	:	Amount
Ratio	→	2000	:	2420
		100	:	121

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

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

		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 ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} Principal  =  Rs 2000 \\ Amount  =  Rs 2420 \\ Rate  =  10% \\ By using formula, \\ \Rightarrow 2420 = 2000 {(1 + \frac{10}{100})}^{n} \\ \Rightarrow \frac{2420}{2000} = {(1 + \frac{10}{100})}^{n} \\ \Rightarrow \frac{121}{100} = {(\frac{11}{10})}^{n} \\ \Rightarrow {(\frac{11}{10})}^{2} = {(\frac{11}{10})}^{n} \\ \Rightarrow n = 2 \\ Hence, \\ required time  =  2 years \end{aligned}

$\eqalign{ & {\text{Principal = Rs 2000}} \cr & {\text{Amount = Rs 2420}} \cr & {\text{Rate = 10% }} \cr & {\text{By using formula,}} \cr & \Rightarrow 2420 = 2000{\left( {1 + \frac{{10}}{{100}}} \right)^n} \cr & \Rightarrow \frac{{2420}}{{2000}} = {\left( {1 + \frac{{10}}{{100}}} \right)^n} \cr & \Rightarrow \frac{{121}}{{100}} = {\left( {\frac{{11}}{{10}}} \right)^n} \cr & \Rightarrow {\left( {\frac{{11}}{{10}}} \right)^2} = {\left( {\frac{{11}}{{10}}} \right)^n} \cr & \Rightarrow n = 2 \cr & {\text{Hence,}} \cr & {\text{required time = 2 years}} \cr}$ Alternative
Note : In such type of questions to save your valuable time follow the given below method.

		Principal	:	Amount
Ratio	→	2000	:	2420
		100	:	121

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

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

		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 ", "dateCreated": "7/24/2019 10:09:12 AM" } }

Test

Classes

E-Book