Question

Simple interest on an amount at \[4\% \] per annum for \[13\] months is more than the simple interest on the same sum for \[8\] months at \[6\% \] per annum by Rs \[40\]. What is the principal amount?

Answer 1

Hint: We need to find the principal amount. Here, we will use the formula of\[SI = \dfrac{{PNR}}{{100}}\]. Where, $P$ is the principal amount, $N$ is the number of years, $R$ is rate of interest per year and SI is the simple interest. Also, Amount = Principal + SI. Simple interest does not compound, meaning that an account holder will only gain interest on the principal, and the borrower will never have to pay the interest on the interest which is already accrued. Also, simple interest is more advantageous for borrowers than compound interest, as it keeps overall interest payments lower.

Complete step by step answer:
We are given data for simple interest. According to question given, we have,
(a) Interest for \[13\] months at \[4\% \]
Given that, Interest per year = \[4\% \]
So, interest per month =\[\dfrac{4}{{12}} = \dfrac{1}{3}\]%
Thus, the interest for 13 months will be
\[\dfrac{1}{3} \times 13 \\
\Rightarrow \dfrac{{13}}{3} \\ \]
(b) Interest for \[8\] months at \[6\% \]
Given that, Interest per year=\[6\% \]
So, the interest per month
\[6 \div 12 \\
\Rightarrow \dfrac{1}{2} \\
\Rightarrow 0.5\% \\ \]
Let the principal amount be Rs $x$.According to the data given in the question, we have,
\[ \Rightarrow \dfrac{{13}}{3}\% of\,x - 4\% ofx = 40\]
\[ \Rightarrow (\dfrac{{13}}{3}\% - 4\% )of\,x = 40\]
Simplify the above expression, we get,
\[\Rightarrow (\dfrac{{13 - 12}}{3})\% of\,x = 40 \\
\Rightarrow \dfrac{1}{3}\% of\,x = 40 \\ \]
Taking the denominator value to the right side of numerator, we get,
\[\Rightarrow 1\% of\,x = 40 \times 3 \\
\Rightarrow 1\% of\,x = 120 \\ \]
As we know that, \[\% = \dfrac{1}{{100}}\]
Thus, substituting the value in the above expression, we get,
\[ \Rightarrow 1 \times \dfrac{1}{{100}}of\,x = 120\]
Taking the denominator value to the right side of numerator, we get,
\[\Rightarrow x = 120 \times 100 \\
\therefore x = 12000\,Rs \]

Thus, the principal amount is Rs \[12000\].

Note:Read the question carefully as what they are asking in the question to find Simple Interest or Compound Interest and solve accordingly. If the interest is calculated uniformly on the original principal throughout the loan period, it is called simple interest. Also, the amount is different for SI and CI. The total money paid back to the lender is called the Amount.