Question

The difference between the compound interest and simple interest on a certain

principal at 10% p.a for 3yrs is rupees 31. Find the principal.​

Answer 1

Given :-

Difference between C.I. and S.I = Rs 31

Rate = 10%

Time = 3 years

To find :-

Principal = ?

Solution :-

Let the sum (Principal) = P

$C.I. =P (\dfrac{r}{100})^n-1 \\ \\ C.I. =P (\dfrac{10}{100})^3-1\\ \\=P ( \dfrac{1331}{1000})-1 \\ \\ =P (\dfrac{1331-1000}{1000}) \\ \\ =P (\dfrac{331}{1000}) \\ \\ C.I.=\dfrac{331}{1000P}$

___________________

$S.I. = \dfrac{P \times R \times T}{100}$

$S.I. = \dfrac{P \times 10 \times 3}{100}$

$S.I. = \dfrac{3P}{10}$

According to the question,

C.I - S.P = Rs 31

$\dfrac{331P}{1000} - \dfrac{3P}{10} = 31$

$\dfrac{331P - 300}{1000} = 31$

$\dfrac{31P}{1000} = 31$

$31P= 31000$

Principal = Rs 1000

Answer 2

$\red{\large{\underline{\underline{ \rm{Problem }}}}}$

The difference between the compound interest and simple interest on a certain principal at 10% per annum for 3yrs is Rs. 31. Find the principal.

$\red{\large{\underline{\underline{ \rm{Given: }}}}}$

Difference between the compound interest and simple interest = Rs. 31

Rate = 10%

Time = 3 years

$\red{\large{\underline{\underline{ \rm{To Find: }}}}}$

Principal

$\red{\large{\underline{\underline{ \rm{Solution: }}}}}$

Refer the attachment ⛈

Let the value of principal be x.

Here first we have found simple interest by using formula and then again by using formula we found the compound interest and then we know that the difference between the compound interest and the simple interest is equal to Rs. 31.

After getting the equation we found the value of x i.e., principal.

$\sf{ \underline{ \boxed{ \sf{S.I. = \frac{P \times R \times T}{100} }}}}$

$\sf{ \underline{ \boxed{ \sf{C.I. = P {\huge[(}{1 + \frac{r}{100} { \huge)}}^{n} - 1{ \huge]}}}}}$

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