Question

If the difference between the simple interest and
compound interest on some principal amount at 20%
per annum for 3 years is 48, then the principle
amount must be
(a) 550
(b) 500
fet 375
(d) 400​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Principal=375\:rupees}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Rate\%(r) = 20\% \\ \\ \tt: \implies Time(t) = 3 \: years \\ \\ \tt: \implies C.I- S.I = 48 \: rupees \\ \\ \red{\underline \bold{to \: find:}}\\ \tt: \implies Principal(p) = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies S.I= \frac{p \times r \times t}{100} \\ \\ \tt: \implies S.I= \frac{p \times 20 \times 3}{100} \\ \\ \tt: \implies S.I= \frac{3p}{5} - - - - - - (1) \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies A =p(1 + \frac{r}{100} )^{t} \\ \\ \tt: \implies A = p(1 + \frac{20}{100} )^{3} \\ \\ \tt: \implies A=p(1 + 0.2)^{3} \\ \\ \tt: \implies A =p \times 1.728\\ \\ \bold{For \: C.I} \\ \tt: \implies C.I =A - p \\ \\ \tt: \implies C.I=1.728p - p \\ \\ \tt: \implies C.I=0.728p - - - - - (2) \\ \\ \bold{As \: according \: to \: question} \\ \tt: \implies C.I - S.I= 48 \\ \\ \tt: \implies 0.728p - 0.6p = 48 \\ \\ \tt: \implies 0.128p =48 \\ \\ \tt: \implies p = \frac{48}{0.128} \\ \\ \green{\tt: \implies p = 375 \: rupees}$

Answer 2

$\huge{\sf {\underline \purple{Answer}}}$

Given that

${ \sf{ \to rate \: of \: interest(r) = 20 percent}} \\ { \sf{ \to time \: taken(t)}} = {\sf{3 \: years}} \\ \to { \sf{compound \: interest \: - simple \: interest = 48 \: rupees}}$

${ \sf{ \underline \purple{We \: need \: to \: find : }}}$

Principle amount = ?

We know that

simple interest (S.I) = prt/100

$\implies{ \sf{S.I = \dfrac{p \times 20 \times3 }{100}}} \\ \implies{ \sf{S.I = \dfrac{3p}{5} = 0.6p }}$

assuming as equation ( 1 )

${ \sf \implies{Annum(A) = p {(1 + \frac{r}{100}) }^{t} }} \\ { \sf{ \implies A = p( {1 + \frac{20}{100} )}^{3} }} \\ { \sf{ \implies A = p{( \frac{6}{5} ) }^{3} }} \\ { \sf{ \implies A = p(1.728)}}$

For compound interest (C.I.)

${ \sf{ \implies \:C.I =A - p }} \\ \\ { \sf{ \implies C.I = 1.728p - p = 0.728}}$

Assuming as equation ( 2 )

According to the question:

C.I. - S.I. = 48

0.728p - 0.6p = 48

0.128p = 48

p = 48/0.128

p = 48000/128

p = 375 ₹

${\boxed{ \rm \orange{principle \: amount \: = \: 375 rupees}}}$