Question

A man borrowed Rs. 200 and paid back
Rs. 250 after 2 years. The rate of interest
per annum is
(a) 10%
(b) 20%
(c) 25%
(d) 12.5%​

Answer 1

Answer:

12.5%

Step-by-step explanation:

Rate= I*100/P*T

= 50*100/200*2

=25/2

=12.5

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Answer 2

Answer:

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{gray}{Given:}}}}}}}\end{gathered}$

• $\red\bigstar$ Interest = 250
• $\red\bigstar$ Principle = 200
• $\red\bigstar$ Time = 2 years

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{gray}{To Find:}}}}}}}\end{gathered}$

• $\red\bigstar$ Rate

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{gray}{Using Formula:}}}}}}}\end{gathered}$

$\dag\underline{\boxed{\sf{SI = A - P}}}$

Where

• $\green\star$ S.I = Simple Interest
• $\green\star$ A = Amount
• $\green\star$ P = Principle

$\dag{\underline{\boxed{\sf{Rate = {\dfrac{S.I \times 100}{P \times T}}}}}}$

Where

• $\green\star$ S.I = Simple Interest
• $\green\star$ P = Principle
• $\green\star$ T = Time

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{gray}{Solution:}}}}}}}\end{gathered}$

${\bigstar \:{\underline{\pmb{\frak{\red{Firstly,Finding \: the \: Simple \: Interest}}}}}}$

$\quad:\implies{\sf{S.I = A - P}}$

• Substituting the values

$\quad:\implies{\sf{S.I = 250 - 200}}$

$\quad:\implies{\sf{S.I = Rs.50}}$

$\begin{gathered} \dag{\boxed{\textsf{\textbf{\underline{\color{green}{Simple Interest = Rs.50}}}}}}\end{gathered}$

• Simple Interest = Rs.50

$\begin{gathered}\end{gathered}$

${\bigstar \:{\underline{\pmb{\frak{\red{ Now,Finding \: The \: Rate \: of \: Interest }}}}}}$

$\quad{: \implies{\sf{Rate = \bf{\dfrac{S.I \times 100}{P \times T}}}}}$

• Substituting the values

$\quad{: \implies{\sf{Rate = \bf{\dfrac{50 \times 100}{200 \times 2}}}}}$

$\quad{: \implies{\sf{Rate =\bf{\dfrac{5000}{400}}}}}$

$\quad{: \implies{\sf{Rate =\bf{\cancel{\dfrac{5000}{400}}}}}}$

$\quad{: \implies{\sf{Rate =\bf{12.5 \%}}}}$

$\begin{gathered} \dag{\boxed{\textsf{\textbf{\underline{\color{green}{Rate = 12.5\%}}}}}}\end{gathered}$

${\therefore{\underline{\sf{Hence, The \: Rate \: of \: Interest \: per \: annum \: is \: 12.5\%}}}}$

$\begin{gathered}\end{gathered}$

$\begin{gathered}{\Large{\textsf{\textbf{\underline{\underline{\color{gray}{Learn More:}}}}}}}\end{gathered}$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \dag \: \underline{\bf{More \: Useful \: Formula}}\\ {\boxed{\begin{array}{cc}\dashrightarrow {\sf{Amount = Principle + Interest}} \\ \\ \dashrightarrow \sf{ P=Amount - Interest }\\ \\ \dashrightarrow \sf{ S.I = \dfrac{P \times R \times T}{100}} \\ \\ \dashrightarrow \sf{P = \dfrac{Interest \times 100 }{Time \times Rate}} \\ \\ \dashrightarrow \sf{P = \dfrac{Amount\times 100 }{100 + (Time \times Rate)}} \\ \end{array}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$