Question

What is the present worth of Rs.$330$/- due $2.5$ years hence, reckoning simple interest at $4\%$ per annum.?
A. Rs.$250$/-
B. Rs.$275$/-
C. Rs.$290$/-
D. Rs.$300$/-
E. None of these

Answer 1

Hint: We have the values of total amount$\left( A \right)$, time period in years$\left( T \right)$ and the rate of interest$\left( R \right)$ in percentage, so the relation between these variables is given by $I=\dfrac{PRT}{100}$ where $P$ is the principle amount. We have also relation between total amount, interest, principle amount as $A=P+I$. First we will assume the principle amount as $x$ and calculate the value of Interest, from the value of interest we will use the equation $A=P+I$ to get the principle amount.

Complete step-by-step answer:
Given that,
Total amount $A=330$
Time period $T=2.5$ years
Rate of Interest $R=4\%$.
Let the principle amount is $P=x$.
Now the simple interest for the principle amount can be calculate by $I=\dfrac{PRT}{100}$.
$\begin{align}
  & \Rightarrow I=\dfrac{x\times 4\times 2.5}{100} \\
 & \Rightarrow I=\dfrac{x\times 10}{100} \\
 & \Rightarrow I=\dfrac{x}{10} \\
\end{align}$
Now the total amount can be given by
$A=P+I$
Substituting the all the values we have then we will get
$330=\dfrac{x}{10}+x$
Taking $x$ common from $\dfrac{x}{10}+x$, then we will get
$\Rightarrow 330=x\left( \dfrac{1}{10}+1 \right)$
We know that $\dfrac{1}{10}=0.1$, then we will get
$\begin{align}
  & \Rightarrow 330=x\left( 0.1+1 \right) \\
 & \Rightarrow 330=1.1x \\
\end{align}$
Dividing the above equation with $1.1$ on both sides of the equation, then we will get
$\begin{align}
  & \Rightarrow \dfrac{330}{1.1}=\dfrac{1.1x}{1.1} \\
 & \Rightarrow x=300 \\
\end{align}$
$\therefore $ The principal amount is Rs.$300$/-

So, the correct answer is “Option D”.

Note:We can also solve the problem by taking the value of principle amount $P$ from known relation $A=P+I$ and substituting it in $I=\dfrac{PRT}{100}$.
Now the value of $P$ from $A=P+I$ is
$P=A-I$
Substituting the value of $P$ in $I=\dfrac{PRT}{100}$, then we will have
$\begin{align}
  & I=\dfrac{PRT}{100} \\
 & \Rightarrow I=\dfrac{\left( A-I \right)RT}{100} \\
 & \Rightarrow I=\dfrac{\left( 330-I \right)4\times 2.5}{100} \\
 & \Rightarrow I=\dfrac{\left( 330-I \right)\times 10}{100} \\
 & \Rightarrow I=\dfrac{330-I}{10} \\
 & \Rightarrow 10I=330-I \\
 & \Rightarrow 11I=330 \\
 & \Rightarrow I=\dfrac{330}{11}=300 \\
\end{align}$
From both the methods we got the same value.