Question

What is the difference between C.I and S.I for the sum of 20000 over a 2 year period, if the C.I is
calcuted at 20% p.a and S.I is calculated at 23% p.a?
A. 350
B. 400 C. 8000 D. 9000 E. 5000
​

Answer 1

Answer :

B. 400 is the correct answer.

Answer 2

Case :- 1 Calculation of Compound Interest

$\begin{gathered}\begin{gathered}\bf Given -  \begin{cases} &\sf{Principal \: = \: Rs \: 20000} \\ &\sf{Rate \: = \: 20 \: \% \: per \: annum} \\ &\sf{Time \: = \: 2 \: years} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf  To \:  Find :-  \begin{cases} &\sf{Compound \: Interest}  \end{cases}\end{gathered}\end{gathered}$

${\large{\bold{\rm{\underline{Using \; formulas}}}}}$

${\sf{\star \: Amount \: = P(1+ \dfrac{R}{100})^{n}}} \: ⋆$

where,

• P denotes Principal

• R denotes Rate

• n denotes time

${\sf{\star CI \: = Amount \: - Principal}} \star$

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

☆ Principal, P = Rs 20000

☆ Rate of interest, R = 20 % per annum

☆ Time = 2 years

$\tt \:  \longrightarrow \: Amount \: = P(1+ \dfrac{R}{100})^{n}$

$\tt \:  \longrightarrow \: Amount \: = 20000 \times (1+ \dfrac{20}{100})^{2}$

$\tt \:  \longrightarrow \: Amount \: = 20000 \times (1+ \dfrac{1}{5})^{2}$

$\tt \:  \longrightarrow \: Amount \: = 20000 \times (\dfrac{6}{5})^{2}$

$\tt \:  \longrightarrow \: Amount \: = 20000 \times \dfrac{6}{5} \times \dfrac{6}{5}$

$\tt \:  \longrightarrow \: Amount \: = \: Rs \: 28800$

$\tt \:  \longrightarrow \: { CI \: = Amount \: - Principal}$

$\tt \:  \longrightarrow \: { CI \: = 28800 \: - \: 20000}$

$\tt \:  \longrightarrow \: { CI \: = Rs \: 8800 }$

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Case :- 2 Calculation of Simple interest

$\begin{gathered}\begin{gathered}\bf Given -  \begin{cases} &\sf{Principal \: = \: Rs \: 20000} \\ &\sf{Rate \: = \: 23 \: \% \: per \: annum} \\ &\sf{Time \: = \: 2 \: years} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf  To \:  Find :-  \begin{cases} &\sf{Simple \: interest}  \end{cases}\end{gathered}\end{gathered}$

${\large{\bold{\rm{\underline{Using \; formulas}}}}}$

${\sf{\star \: Simple \: interest \: = \: \dfrac{P \times R \times T}{100}}} \: ⋆$

where,

• P denotes Principal

• R denotes Rate

• T denotes time

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

☆ Principal, P = Rs 20000

☆ Rate of interest, R = 23 % per annum

☆ Time = 2 years

$\tt \:  \longrightarrow \: Simple \: interest \: = \: \dfrac{P \times R \times T}{100}$

$\tt \:  \longrightarrow \: Simple \: interest \: = \: \dfrac{20000 \times 23 \times 2}{100}$

$\tt \:  \longrightarrow \: Simple \: interest \: = \: Rs \: 9200$

$\tt\implies \:Difference \: = \: Rs \: 9200 - Rs8800$

$\tt\implies \:Difference \: = \: Rs \: 400$

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$\large{\boxed{\boxed{\bf{Option \: (b) \: is \: correct}}}}$

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