The difference between the CI compounded annually and the simple interest on a certain sum of two years at 15% per annum is Rs.180 find the sum
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Answer:
Let principal = Rs 'x'
\begin{gathered}SI=\dfrac{P\times R\times T}{100}\\\\\\SI=\dfrac{x\times15\times2}{100}\\\\\\=\dfrac{3x}{10}\\\\\\CA=P\:\bigg(1+\dfrac{r}{100}\bigg)^t\\\\\\=x\bigg(1+\dfrac{15}{100}\bigg)^2\\\\\\=\dfrac{529}{400}x\\\\\\CI=\dfrac{529}{400}x-x\\\\\\=\dfrac{129}{400}x\end{gathered}
SI=
100
P×R×T
SI=
100
x×15×2
=
10
3x
CA=P(1+
100
r
)
t
=x(1+
100
15
)
2
=
400
529
x
CI=
400
529
x−x
=
400
129
x
According to the question
\begin{gathered}CI-SI=180\\\\\\\implies\dfrac{129x-120x}{400}=180\\\\\\\implies9x=180\times400\\\\\\\implies x=\dfrac{180\times400}{9}\\\\\\\implies \boxed{\bold{x=Rs.\:8000\:answer}}\end{gathered}
CI−SI=180
⟹
400
129x−120x
=180
⟹9x=180×400
⟹x=
9
180×400
⟹
x=Rs.8000answer
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