Question

the difference in simple interest and compound interest on a certain sum of money at 10% per annum rate of interest for 2 years is rupees 10 find the sum​

Answer 1

Appropriate Question:

The difference in compound interest and simple interest on a certain sum of money at 10% per annum rate of interest, for 2 years is rupees 10, find the sum.

Answer:

$\boxed{\sf \: Sum\:invested\:is\:Rs\:1000 \: }$

Explanation:

Given that,

Rate of interest, r = 10 % per annum

Time period, n = 2 years

Difference between CI and SI = Rs 10

Let assume that sum invested be Rs P.

Now, it is given that

$\sf \: CI - SI = 10$

$\sf \: P {\bigg[1 + \dfrac{r}{100} \bigg]}^{n}  - P - \dfrac{P \times r \times n}{100}  = 10$

On substituting the values, we get

$\sf \: P {\bigg[1 + \dfrac{10}{100} \bigg]}^{2}  - P - \dfrac{P \times 10 \times 2}{100}  = 10$

$\sf \: P {\bigg[1 + \dfrac{1}{10} \bigg]}^{2}  - P - \dfrac{P}{5}  = 10$

$\sf \: P {\bigg[\dfrac{10 + 1}{10} \bigg]}^{2}  - P - \dfrac{P}{5}  = 10$

$\sf \: P {\bigg[\dfrac{11}{10} \bigg]}^{2}  - P - \dfrac{P}{5}  = 600$

$\sf \: \dfrac{121P}{100}   - P - \dfrac{P}{5}  = 10$

$\sf \: \dfrac{121P - 100P - 20P }{100}  = 10$

$\sf \: \dfrac{21P - 20P }{100}  = 10$

$\sf \: \dfrac{P }{100}  = 10$

$\sf \: P = 100 \times 10$

$\sf\implies \sf \: P = 1000$

Hence,

$\sf\implies \sf \: Sum\:invested\:is\:Rs\:1000$

$\rule{190pt}{2pt}$

Additional information

1. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded annually for n years is given by

$\boxed{ \rm{ \:Amount \:  =  \: P \:  {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} \:  \: }}$

2. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded semi - annually for n years is given by

$\boxed{ \rm{ \:Amount \:  =  \: P \:  {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n} \:  \: }}$

3. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded quarterly for n years is given by

$\boxed{ \rm{ \:Amount \:  =  \: P \:  {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} \:  \: }}$

4. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded monthly for n years is given by

$\boxed{ \rm{ \:Amount \:  =  \: P \:  {\bigg[1 + \dfrac{r}{1200} \bigg]}^{12n} \:  \: }}$

Answer 2

Answer:

P=1000rs.

Explanation:

.S.I-C. P (r/100)^2.

10= P(10/100)^2.

10=P(1/100)

P = 10×100

P=1000 rs. (ans.)

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