Question

The simple interest on a certain sum of money for 3 years at 5% per annum is Rs. 1,200. Find the principal amount.

Answer 1

Hint: We here have been given the simple interest on some amount of money after a fixed period of time at a fixed rate and we have been asked to find the principal sum. For this, we will first assume the principal amount to be ‘x’ and then we will use the formula given as follows:
The simple interest, let us assume it to be I, on some principal amount, let us assume it to be P, at the rate ‘R’ for time ‘T’ is given as:
$I=\dfrac{P\times T\times R}{100}$
Then we will put the given values in this formula and solve for x. Hence, we will get our answer.

Complete step by step answer:
We have been given that the simple interest on some principal amount of money after 3 years at the rate of 5% per annum is Rs. 1200 and we have to find the principal amount. For this, we will first assume the principal amount to be ‘x’.
Now, we know that the simple interest, let us assume it to be I, on some principal amount, let us assume it to be P, at the rate ‘R’ for time ‘T’ is given as:
$I=\dfrac{P\times T\times R}{100}$
Now, here we have been given that:
I= 1200
P=x
T= 3
R= 5
Thus, putting these values in this formula we get:
\[\begin{align}
  & I=\dfrac{P\times T\times R}{100} \\
 & \Rightarrow 1200=\dfrac{x\times 3\times 5}{100} \\
\end{align}\]
Solving this, we get:
\[\begin{align}
  & 1200=\dfrac{x\times 3\times 5}{100} \\
 & \Rightarrow 1200=\dfrac{15x}{100} \\
 & \Rightarrow \dfrac{120000}{15}=x \\
 & \therefore x=8000 \\
\end{align}\]

Hence, the principal amount is Rs. 8000.

Note: We here have been given simple interest per annum for 3 years. That’s why time taken is also taken as 3. But, if it was given as half-yearly, then it would have meant that two times once a year, i.e. $3\times 2=6$ years. So, always read the question carefully and make the correct observations.