Question

Find the sum of money when the final amount is Rs. $11300$ at $4\% $ p.a. for $3$ years $3$ months.

Answer 1

Hint: Let us assume the principal to be x. Now the value of amount, rate, and time are given in the question. We will use the formula of simple interest which is given as-$S.I. = \dfrac{{P \times R \times T}}{{100}}$ where P is the principal, R is rate and T is time. Put the given values and solve them to get Simple interest. Then use the formula of Amount which is given as-Amount=Principal +Simple Interest
Put the given values in the formula and solve it to get the value of the Principal.
Complete step-by-step answer:
Given, Amount=$11300$, Rate=$4\% $ and Time= $3$ years $3$ months.
We know that one year has $12$ months then we can write the time as-
T=$3 + \dfrac{3}{{12}}$ years
On solving, we get-
T=$3 + \dfrac{1}{4} = \dfrac{{12 + 1}}{4} = \dfrac{{13}}{4}$years
Let us assume the sum of money (principal) to be Rs x.
Now we know the formula of simple interest is given by-
$ \Rightarrow S.I. = \dfrac{{P \times R \times T}}{{100}}$
On putting the given values in the formula, we get-
$ \Rightarrow S.I. = \dfrac{{x \times 4 \times \dfrac{{13}}{4}}}{{100}}$
On simplifying we get-
$ \Rightarrow $ S.I. =$\dfrac{{x \times 4 \times 13}}{{100 \times 4}}$
On solving we get-
$ \Rightarrow $ S.I. $ = \dfrac{{13x}}{{100}}$
Now, we will use the formula of the amount which is given as-
$ \Rightarrow $ Amount=Principal +Simple Interest
On putting the given values in the formula, we get-
$ \Rightarrow 11300 = x + \dfrac{{13x}}{{100}}$
On taking LCM on the right side, we get-
$ \Rightarrow 11300 = \dfrac{{100x + 13x}}{{100}}$
On adding the terms, we get-
$ \Rightarrow 11300 = \dfrac{{113x}}{{100}}$
On adjusting, we get-
$ \Rightarrow $ x=$\dfrac{{11300 \times 100}}{{113}}$
On simplifying we get-
$ \Rightarrow $ x=$100 \times 100$
On multiplication, we get-
$ \Rightarrow $ x=Rs. $10000$
Hence the sum of money is Rs.$10000$ .

Note: Many students may try to use the formula of the amount directly to solve the given question. Here we cannot use the formula of Amount directly which is given as-
Amount=Principal${\left[ {1 + \left( {\dfrac{{{\text{rate}}}}{{100}}} \right)} \right]^n}$ where n is the time.
Here if we put the given values in the formula we get-
$ \Rightarrow 11300 = x{\left[ {1 + \dfrac{4}{{100}}} \right]^{13/4}}$
We can see that the time here is in a fraction which will make solving the above equation difficult. Hence we have not used this formula to solve the given question.