Question

6.
On what sum of money will the difference between
the simple interest and the compound interest for
2 years at 5% per annum be equal to 50 ?



​

Answer 1

Answer:-

• Rs. 20,000

Explanation :-

Let p is required sum of money.

${ \bigstar{ \underline{According \: to \: the \: question, }}}$

${\sf {Difference \: in \: simple \: interest \: and \: compound \: interest }} \\ { \sf{for \: 2 \: years : - }} \\ \\ \sf \longmapsto \: p \times ({\frac{r}{100} )}^{2} \\ \sf \longmapsto \: 50 = p \times ({ \frac{5}{100}) }^{2} \\\sf \longmapsto \: 50 = p \times \frac{1}{400} \\ \sf \longmapsto \: p = 400 \times 50 \\ \sf \longmapsto \: p = 20000$

${\therefore{ \sf{\: Sum \: of \: money \: is \: Rs \: 20,000.}}}$

Answer 2

$\sf{\huge{\bold{\pink{\bigstar{\boxed{\boxed{Question}}}}}}}$

• On what sum of money will the difference betweenthe simple interest and the compound interest for 2 years at 5% per annum be equal to 50 ?

$\sf{\huge{\bold{\pink{\bigstar{\boxed{\boxed{Solution}}}}}}}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

Rate = 5%

Time = 2years

diff btw. C.I and S.I = Rs.50

$\sf{\bold{\blue{\underline{\underline{To\:find}}}}}$

principle = p = ????

$\sf{\bold{\purple{\underline{\underline{Explanation}}}}}$

$\sf{\bold{\red{\boxed{SI = \dfrac{prt}{100} }}}}$

$\sf{SI = \dfrac{p\times 5\times 2}{100}}$

$\sf{SI = \dfrac{10p}{100}}$

$\sf{\bold{\red{\boxed{CI = P(1 + \dfrac{r}{100})^{time} }}}}$

$\sf{CI = P(1 + \dfrac{5}{100})^2} - P$

$\sf{CI = P(\dfrac{105}{100})^2}- P$

$\sf{CI = \dfrac{11025}{10000} P} - P$

$\sf{CI = \dfrac{11025p - 10000p}{10000}}$

$\sf{CI = \dfrac{1025p}{10000}}$

ATQ :-

CI - SI = 50

$\sf {\dfrac{1025p}{10000} - \dfrac{10p}{100}} = 50$

$\sf{\dfrac{1025p - 1000p}{10000} = 50}$

$\sf{\dfrac{25p}{10000} = 50 }$

$\sf { p = \dfrac{50 \times{ 10000}}{{25}}}$

$\sf{p = \dfrac{\cancel{50}\times 100}{\cancel{25}}}$

$\sf{p = Rs.20000}$

$\sf{\bold{\orange{\boxed{principle = Rs.20000}}}}$

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