GIVEN :-CI - SI = RS. 120.Rate ( R ) = 8 %.Time ( n ) = 2 years.TO FIND :-The Sum.SOLUTION :-LET the Principal be x.Now,Now According to the question,Hence the REQUIRED sum is Rs. 18750.

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The difference between the compound interest and the simple interest for 2 years at 8% per annum on a certain sum of money is 120. Find the sum

Math Secondary School in Math 9 months ago

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GIVEN :-

CI - SI = RS. 120.
Rate ( R ) = 8 %.
Time ( n ) = 2 years.

TO FIND :-

The Sum.

SOLUTION :-

LET the Principal be "x".

$\\ : \implies \displaystyle \sf \: SI = \dfrac{P \times R \times T}{1 00 } \\ \\ \\$

$: \implies \displaystyle \sf \: SI = \frac{x \times 8 \times 2}{100} \\ \\ \\$

$: \implies \underline{\boxed{\displaystyle \sf SI = \frac{16x}{100} }} \\ \\$

Now,

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

$: \implies \displaystyle \sf \: CI = x \Bigg[ \bigg(1 + \dfrac{8}{100}\bigg)^{2} -1\Bigg] \\ \\ \\$

$: \implies \displaystyle \sf \: CI = x \Bigg[ \bigg( \dfrac{100 + 8}{100}\bigg)^{2} -1\Bigg] \\ \\ \\$

$: \implies \displaystyle \sf \: CI = x \Bigg[ \bigg( \dfrac{108}{100}\bigg)^{2} -1\Bigg] \\ \\ \\$

$: \implies \displaystyle \sf \: CI = x \Bigg[\dfrac{108 \times 108}{100 \times 100} -1\Bigg] \\ \\ \\$

$: \implies \displaystyle \sf \: CI = x \Bigg[\dfrac{11664}{10000} -1\Bigg] \\ \\ \\$

$: \implies \displaystyle \sf \: CI = x \Bigg[\dfrac{11664 - 10000}{10000}\Bigg] \\ \\ \\$

$: \implies \displaystyle \sf \: CI = x \Bigg[\dfrac{1664 }{10000}\Bigg] \\ \\ \\$

$: \implies \displaystyle \sf \: CI = x \times \frac{1664}{10000} \\ \\ \\$

$: \implies \underline{ \boxed{ \displaystyle \sf \: CI = \frac{1664x}{10000} }} \\ \\$

Now According to the question,

$\\ \\ : \implies \displaystyle \sf \: CI - SI = 120 \\ \\ \\$

$: \implies \displaystyle \sf \: \frac{1664x}{10000} - \frac{16x}{100} = 120 \\ \\ \\$

$: \implies \displaystyle \sf \: \frac{1664x}{10000} - \frac{1600x}{10000} = 120 \\ \\ \\$

$: \implies \displaystyle \sf \: \frac{1664x - 1600x}{10000} = 120 \\ \\ \\$

$: \implies \displaystyle \sf \: \frac{64x}{10000} = 120 \\ \\ \\$

$: \implies \displaystyle \sf \:64x = 120 \times 10000 \\ \\ \\$

$: \implies \displaystyle \sf \:64x = 1200000 \\ \\ \\$

$: \implies \displaystyle \sf \:x = \frac{1200000}{64} \\ \\ \\$

$: \implies \underline{ \boxed{ \displaystyle \sf \:x = 18750}} \\ \\$

Hence the REQUIRED sum is Rs. 18750.

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Posted on 25 Oct 2024, this text provides information on Math related to Secondary School in Math. Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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The difference between the compound interest and the simple interest for 2 years at 8% per annum on a certain sum of money is 120. Find the sum