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Simple interest on a certain sum at a certain annual rate of interest is $\frac{1}{9}$ $\frac{1}{9}$ of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is -

1 $3 \frac{1}{3}$ $3\frac{1}{3}$ %
25%
3 $6 \frac{2}{3}$ $6\frac{2}{3}$ %
410%

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let sum = x \\ Then, \\ S .I . = \frac{x}{9} . \\ Let rate = R % and \\ time = R years . \\ ∴ (\frac{x \times R \times R}{100}) = \frac{x}{9} \\ \Rightarrow R^{2} = \frac{100}{9} \\ \Rightarrow R = \frac{10}{3} = 3 \frac{1}{3} \\ Hence, rate = 3 \frac{1}{3} % \end{aligned}

$\eqalign{ & {\text{Let sum}} = x \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{x}{9}. \cr & {\text{Let rate}} = {\text{R}}\% \,{\text{and}} \cr & {\text{time}} = {\text{R}}\,{\text{years}}{\text{.}} \cr & \therefore \left( {\frac{{x \times {\text{R}} \times {\text{R}}}}{{100}}} \right) = \frac{x}{9} \cr & \Rightarrow {{\text{R}}^2} = \frac{{100}}{9} \cr & \Rightarrow {\text{R}} = \frac{{10}}{3} = 3\frac{1}{3} \cr & {\text{Hence, rate}} = 3\frac{1}{3}\% \cr}$

02. A person deposits Rs. 500 in 4 years and Rs. 600 for 3 years at the same rate of simple interest in a bank. Altogether he received Rs. 190 as interest. The rate of simple interest per annum was = ?

14%
25%
32%
43%

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Answer:- 1

Explanation:-

Solution:

Let rate of interest = R%
According to the question,

\begin{aligned} \frac{500 \times 4 \times R}{100} + \frac{600 \times 3 \times R}{100} = 190 \\ \Rightarrow 20 R + 18R  =  190 \\ \Rightarrow 38 R  =  190 \\ \Rightarrow R  =  5% \end{aligned}

$\eqalign{ & \frac{{500 \times 4 \times {\text{R}}}}{{100}} + \frac{{600 \times 3 \times {\text{R}}}}{{100}} = 190 \cr & \Rightarrow 20{\text{R + 18R = 190}} \cr & \Rightarrow 38{\text{R = 190}} \cr & \Rightarrow {\text{R = 5% }} \cr}$
Hence required rate % = 5%

Alternate
Note : In such type of questions to save your valuable time follow the given below method.
Let rate of interest = 1%

\begin{aligned} Case (I): Interest (I_{1}) \\ = \frac{500 \times 4 \times 1}{100} \\ = 20 \\ Case (II): Interest (I_{2}) \\ = \frac{600 \times 3 \times 1}{100} \\ = 18 \end{aligned}

$\eqalign{ & {\text{Case (I): Interest (}}{{\text{I}}_1}{\text{)}} \cr & {\text{ = }}\frac{{500 \times 4 \times 1}}{{100}} \cr & = 20 \cr & {\text{Case (II): Interest (}}{{\text{I}}_2}{\text{)}} \cr & {\text{ = }}\frac{{{\text{600}} \times 3 \times 1}}{{100}} \cr & = 18 \cr}$
According to the question,

Interest	Rate %
38	1
↓×5	↓×5
190	5%

Hence required rate % = 5%

03. A certain scheme of investment in simple interest declares that it triples the investment in 8 years. If you want to quadruple the money through that scheme for how many years you have to invest for = ?

111 years 6 months
210 years 8 months
310 years
412 years

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} P + \frac{P \times r \times t}{100} = 3 P \\ \Rightarrow 1 + \frac{r t}{100} = 3 \\ \Rightarrow \frac{rt}{100} = 2 \\ \Rightarrow r = \frac{2 \times 100}{8} = 25 % \\ so, (1 + \frac{rt}{100}) = 4 \\ \Rightarrow \frac{rt}{100} = 3 \\ \Rightarrow t = \frac{3 \times 100}{25} \\ \Rightarrow t = 12 years \end{aligned}

$\eqalign{ & {\text{P}} + \frac{{P \times {\text{r}} \times {\text{t}}}}{{100}} = 3{\text{P}} \cr & \Rightarrow 1 + \frac{{rt}}{{100}} = 3 \cr & \Rightarrow \frac{{{\text{rt}}}}{{100}} = 2 \cr & \Rightarrow {\text{r}} = \frac{{2 \times 100}}{8} = 25\% \cr & {\text{so, }}\,\left( {1 + \frac{{{\text{rt}}}}{{100}}} \right) = 4 \cr & \Rightarrow \frac{{{\text{rt}}}}{{100}} = 3 \cr & \Rightarrow {\text{t}} = \frac{{3 \times 100}}{{25}} \cr & \Rightarrow {\text{t}} = 12\,{\text{years}} \cr}$

04. A person invests Rs. 12000 as fixed deposit at a bank at the rate of 10% per annum simple interest. But due to some pressing needs he has to withdraw the entire money after three years, for which the bank allowed him a lower rate of interest. If he gets Rs. 3320 less than what he would have got at the end of 5 years, the rate of interest allowed by the bank is = ?

1 $7 \frac{5}{9}$ ${\text{7}}\frac{5}{9}$ %
2 $7 \frac{4}{9}$ ${\text{7}}\frac{4}{9}$ %
3 $7 \frac{8}{9}$ ${\text{7}}\frac{8}{9}$ %
4 $8 \frac{7}{9}$ ${\text{8}}\frac{7}{9}$ %

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Answer:- 1

Explanation:-

Solution:

Principal = Rs. 12000
Rate % = 10%
Interest paid by the person in 5 years

\begin{aligned} = \frac{12000 \times 10 \times 5}{100} \\ = Rs . 6000 \end{aligned}

$\eqalign{ & = \frac{{12000 \times 10 \times 5}}{{100}} \cr & = {\text{Rs}}{\text{. 6000}} \cr}$
Interest received by the person after 3 years

\begin{aligned} = Rs . (6000 - 3320) \\ = Rs . 2680 \\ By using formula, \\ Rate % \\ = \frac{2680}{12000} \times \frac{100}{3} \\ = \frac{67}{9} \\ = 7 \frac{4}{9} % \\ Hence required rate % \\ =  7 \frac{4}{9} % \end{aligned}

$\eqalign{ & = {\text{Rs}}{\text{. }}\left( {6000 - 3320} \right) \cr & = {\text{Rs}}{\text{. 2680}} \cr & {\text{By using formula,}} \cr & {\text{Rate}}\% \cr & {\text{ = }}\frac{{2680}}{{12000}} \times \frac{{100}}{3} \cr & = \frac{{67}}{9} \cr & = 7\frac{4}{9}\% \cr & {\text{Hence required rate}}\% \cr & {\text{ = 7}}\frac{4}{9}\% \cr}$

05. A person who pays income tax at the rate of 4 paise per rupee, find that fall of interest rate (income tax) from 4% to 3.75% diminishes his net yearly income by Rs. 48. What is his capital ?

1Rs. 24000
2Rs. 25000
3Rs. 20000
4Rs. 18000

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Answer:- 1

Explanation:-

Solution:

Capital after paying income tax

\begin{aligned} \Rightarrow 4 % - 3 .75 % = 48 \\ \Rightarrow 0 .25 % =  48 \\ 100 % = \frac{48}{0.25} \times 100 \\ = 19200 \end{aligned}

$\eqalign{ & \Rightarrow {\text{4}}\% - {\text{3}}{\text{.75}}\% = {\text{48}} \cr & \Rightarrow {\text{0}}{\text{.25}}\% {\text{ = 48}} \cr & {\text{100}}\% {\text{ = }}\frac{{48}}{{0.25}} \times 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 19200 \cr}$
⇒ Capital without paying income tax

\begin{aligned} 19200 = Capital \times 96 % \\ Net capital  =  20000 \end{aligned}

$\eqalign{ & {\text{19200}} = {\text{Capital}} \times {\text{96}}\% \cr & {\text{Net capital = 20000}} \cr}$

06. The population of a village decreases at the rate of 20% per annum. If its population 2 years ago was 10000, the present population is = ?

14600
26400
37600
46000

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} Present Population \\ = P {(\frac{1 - R}{100})}^{n} \\ = 10000 {(\frac{1 - 20}{100})}^{2} \\ = 10000 {(\frac{100 - 20}{100})}^{2} \\ = 10000 {(\frac{80}{100})}^{2} \\ = 10000 {(\frac{4}{5})}^{2} \\ = 10000 \times \frac{16}{25} \\ = 400 \times 16 \\ = 6400 \end{aligned}

$\eqalign{ & {\text{Present Population}} \cr & = {\text{P}}{\left( {\frac{{1 - {\text{R}}}}{{100}}} \right)^n} \cr & = 10000{\left( {\frac{{1 - 20}}{{100}}} \right)^2} \cr & = 10000{\left( {\frac{{100 - 20}}{{100}}} \right)^2} \cr & = 10000{\left( {\frac{{80}}{{100}}} \right)^2} \cr & = 10000{\left( {\frac{4}{5}} \right)^2} \cr & = 10000 \times \frac{{16}}{{25}} \cr & = 400 \times 16 \cr & = 6400 \cr}$

07. In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum?

1 $1 \frac{1}{4}$ $1\frac{1}{4}$ years
2 $1 \frac{3}{4}$ $1\frac{3}{4}$ years
3 $2 \frac{1}{4}$ $2\frac{1}{4}$ years
4 $2 \frac{3}{4}$ $2\frac{3}{4}$ years

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let sum = x . \\ Then, \\ S .I . = 0.125 x = \frac{1}{8} x \\ R = 10 % \\ ∴ R a t e \\ = (\frac{100 \times x}{x \times 8 \times 10}) years \\ = \frac{5}{4} years \\ = 1 \frac{1}{4} years \end{aligned}

$\eqalign{ & {\text{Let sum}} = x. \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = 0.125x = \frac{1}{8}x \cr & {\text{R}} = 10\% \cr & \therefore Rate \cr & = \left( {\frac{{100 \times x}}{{x \times 8 \times 10}}} \right){\text{years}} \cr & = \frac{5}{4}{\text{years}} \cr & = {\text{1}}\frac{1}{4}{\text{years}} \cr}$

08. The simple interest on a sum of money at 8% per annum for 6 years is half the sum. The sum is:

1Rs. 4800
2Rs. 6000
3Rs. 8000
4Date inadequate

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let sum = x . \\ Then, \\ S .I . = \frac{x}{2} . \\ ∴ \frac{x}{2} = \frac{x \times 8 \times 6}{100} . \end{aligned}

$\eqalign{ & {\text{Let sum}} = x{\text{.}} \cr & {\text{Then,}} \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{x}{2}. \cr & \therefore \frac{x}{2} = \frac{{x \times 8 \times 6}}{{100}}. \cr}$
Clearly, data is inadequate.

09. In what time will Rs. 1860 amount to 2641.20 at simple interest 12% per annum ?

13 years
2 $3 \frac{1}{2}$ $3\frac{1}{2}$ years
34 years
4 $4 \frac{1}{2}$ $4\frac{1}{2}$ years

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} Rate % = 2 % \\ Principal  =  Rs . 1860 \\ Amount  =  Rs . 2641 .20 \\ Interest \\ =  Rs . (2641.20 - 1860) \\ = Rs . 781 .20 \\ By using formula, \\ Required time \\ = \frac{781.20 \times 100}{1860 \times 12} \\ = 3 \frac{1}{2} years \end{aligned}

$\eqalign{ & {\text{Rate }}\% = {\text{2}}\% \cr & {\text{Principal = Rs}}{\text{. 1860}} \cr & {\text{Amount = Rs}}{\text{. 2641}}{\text{.20}} \cr & {\text{Interest}} \cr & {\text{ = Rs}}{\text{. }}\left( {2641.20 - 1860} \right) \cr & = {\text{Rs}}{\text{. 781}}{\text{.20}} \cr & {\text{By using formula,}} \cr & {\text{Required time }} \cr & = \frac{{781.20 \times 100}}{{1860 \times 12}} \cr & = 3\frac{1}{2}{\text{ years}} \cr}$

10. In a certain time, the ratio of a certain principal and interest obtained from it are in the ratio 10:3 at 10% interest per annum. The number of years for which the money was invested is = ?

11 year
23 year
35 year
47 year

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Answer:- 1

Explanation:-

Solution:

According to the question

Principal	Interest
10	3

\begin{aligned} Rate % =  10 % \\ Time  = \frac{3}{10} \times \frac{100}{10} \\ = 3 years \end{aligned}

$\eqalign{ & {\text{Rate }}\% {\text{ = 10}}\% \cr & {\text{Time = }}\frac{3}{{10}} \times \frac{{100}}{{10}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 3\,{\text{years}} \cr}$

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Simple Interest - 03

Simple interest on a certain sum at a certain annual rate of interest is $\frac{1}{9}$ $\frac{1}{9}$ of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is -

02. A person deposits Rs. 500 in 4 years and Rs. 600 for 3 years at the same rate of simple interest in a bank. Altogether he received Rs. 190 as interest. The rate of simple interest per annum was = ?

03. A certain scheme of investment in simple interest declares that it triples the investment in 8 years. If you want to quadruple the money through that scheme for how many years you have to invest for = ?

05. A person who pays income tax at the rate of 4 paise per rupee, find that fall of interest rate (income tax) from 4% to 3.75% diminishes his net yearly income by Rs. 48. What is his capital ?

06. The population of a village decreases at the rate of 20% per annum. If its population 2 years ago was 10000, the present population is = ?

07. In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum?

08. The simple interest on a sum of money at 8% per annum for 6 years is half the sum. The sum is:

09. In what time will Rs. 1860 amount to 2641.20 at simple interest 12% per annum ?

10. In a certain time, the ratio of a certain principal and interest obtained from it are in the ratio 10:3 at 10% interest per annum. The number of years for which the money was invested is = ?

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NCERT
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Simple Interest - 03

01. Simple interest on a certain sum at a certain annual rate of interest is 1919\frac{1}{9} of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is -

02. A person deposits Rs. 500 in 4 years and Rs. 600 for 3 years at the same rate of simple interest in a bank. Altogether he received Rs. 190 as interest. The rate of simple interest per annum was = ?

03. A certain scheme of investment in simple interest declares that it triples the investment in 8 years. If you want to quadruple the money through that scheme for how many years you have to invest for = ?

05. A person who pays income tax at the rate of 4 paise per rupee, find that fall of interest rate (income tax) from 4% to 3.75% diminishes his net yearly income by Rs. 48. What is his capital ?

06. The population of a village decreases at the rate of 20% per annum. If its population 2 years ago was 10000, the present population is = ?

07. In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum?

08. The simple interest on a sum of money at 8% per annum for 6 years is half the sum. The sum is:

09. In what time will Rs. 1860 amount to 2641.20 at simple interest 12% per annum ?

10. In a certain time, the ratio of a certain principal and interest obtained from it are in the ratio 10:3 at 10% interest per annum. The number of years for which the money was invested is = ?

Subject Wise

Exam Wise

NCERT 6 to 12

Paid Course

Practice Batch

Simple interest on a certain sum at a certain annual rate of interest is $\frac{1}{9}$ $\frac{1}{9}$ of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is -

NCERT
6 to 12