Question

What is the rate of simple interest if interest is $Rs\,800$ for the sum of $Rs\,4000$ after two years.

Answer 1

Hint: The problem can be solved easily with the concept of simple interest. Interest is the amount of money gained on the principal over a certain period of time. In simple interest, the principal amount over which the interest is calculated remains the same over time. We will substitute the values of the known quantities into the formula for simple interest to find the rate of interest.

Complete step by step answer:
In the given problem,
Principal $ = P = Rs\,4000$
Rate of interest $ = R\% $
Time Duration $ = T = 2\,years$
Also, we are given the simple interest as $Rs\,800$.
Now, we know the formula for simple interest earned over the principal amount P over the time period T at rate of interest R as: $Interest = \dfrac{{P \times R \times T}}{{100}}$.
So, substituting the value of known quantities such as principal, time duration, and simple interest, we get,
$Rs800 = \dfrac{{Rs4000 \times R \times 2}}{{100}}$
Shifting the terms in the equation and simplifying the calculations, we get,
\[ \Rightarrow \dfrac{{800 \times 100}}{{4000 \times 2}} = R\]
Cancelling common factors in numerator and denominator, we get,
\[ \Rightarrow R = \dfrac{{800}}{{80}}\]
\[ \Rightarrow R = 10\]
Hence, the value of R is \[10\].
Thus, the rate of simple interest is \[10\% \] if interest is $Rs\,800$ for the sum of $Rs\,4000$ after two years.

Note:
In case of compound interest, the principal amount over which the interest is calculated keeps on increasing with time period. Whereas, in simple interest, the principal amount remains constant. We can also solve the given question with a shortcut technique. We know that \[10\% \] of the principal amount $Rs\,4000$ is $Rs\,400$. Also, we are given the simple interest earned as $Rs\,800$. As we know, the simple interest earned over a principal amount remains fixed every year. So, we can conclude that we will get $Rs\,800$ as simple interest at the end of two years.