Question

the difference between SI and cI on a certain sum for 2years at 5% per annum is rs26 find the sum.


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Answer 1

GIVEN :-

• C.I - S.I = Rs. 26
• Rate , R = 5% Per annum.
• Time , T = 2 years.

TO FIND :-

• The sum , P.

SOLUTION :-

Let the sum be "x".

Now as we know that this formula of simple interest is given by,

$\\ : \implies \displaystyle \sf \: S.I = \frac{P \times R \times T}{100}$

$: \implies \displaystyle \sf \: S.I = \frac{x \times 5 \times 2}{100}$

$: \implies \displaystyle \sf \: S.I = \frac{10x}{100}$

$: \implies \underline{ \boxed{\displaystyle \sf \: S.I = \frac{x}{10} }} \: \: \: \: \: \: \: \: \: \: \: \: \bigg \lgroup \displaystyle \sf \:Equation \: 1\bigg \rgroup$

Now as we know that the formula for finding the compound interest is given by,

$\\ : \implies \displaystyle \sf \: C.I = P\Bigg[\bigg(1 + \dfrac{R}{100} \bigg)^{n} - 1\Bigg]$

$: \implies \displaystyle \sf \: C.I = x\Bigg[\bigg(1 + \dfrac{5}{100} \bigg)^{2} - 1\Bigg]$

$: \implies \displaystyle \sf \: C.I = x\Bigg[\bigg( \dfrac{100 + 5}{100} \bigg)^{2} - 1\Bigg]$

$: \implies \displaystyle \sf \: C.I = x\Bigg[\bigg( \dfrac{105}{100} \bigg)^{2} - 1\Bigg]$

$: \implies \displaystyle \sf \: C.I = x\Bigg[\bigg( \dfrac{105 \times 105}{100 \times 100} \bigg)- 1\Bigg]$

$: \implies \displaystyle \sf \: C.I = x\Bigg[\dfrac{11025}{10000} - 1\Bigg]$

$: \implies \displaystyle \sf \: C.I = x\Bigg[\dfrac{11025 - 10000}{10000} \Bigg]$

$: \implies \displaystyle \sf \: C.I = x\Bigg[\dfrac{1025}{10000} \Bigg]$

$: \implies \underline{ \boxed{ \displaystyle \sf \: C.I = \frac{1025x}{10000} }} \: \: \: \: \: \: \: \: \: \: \bigg \lgroup \displaystyle \sf \:Equation \: 2\bigg \rgroup$

Now , According to question we have the difference between the compound interest and the simple interest . So,

$\\ : \implies \displaystyle \sf \: C.I - S.I = 26$

$: \implies \displaystyle \sf \: \frac{1025x}{10000} - \frac{x}{10} = 26$

$: \implies \displaystyle \sf \: \frac{1025 x- 1000x }{10000} = 26$

$: \implies \displaystyle \sf \: \frac{25x}{10000} = 26$

$: \implies \displaystyle \sf \:25x = 26 \times 10000$

$: \implies \displaystyle \sf \:25x = 260000$

$: \implies \displaystyle \sf \:x = \frac{260000}{25}$

$: \implies \underline{ \boxed{ \displaystyle \sf \:x = 10400}}$

Hence the required sum of money is Rs. 10400