Question

Mr. Gupta borrowed a sum of money on compound interest. What will be the amount to be repaid if he is paying the entire amount at the end of two years? Which of the following statements is redundant?
I. The interest fetched on the same amount in one year is $Rs\,600$.
II. Simple interest fetched on the same amount in one year is $Rs\,600$.
III. The amount borrowed is ten times the simple interest in two years.

Answer 1

Hint: The problem can be solved easily with the concept of simple interest and compound interest. Interest is the amount of money gained on the principal over a certain period of time. The formula of compound interest on a principal $P$ at the rate of interest $R$ for a time period $T$ is $P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$. Also, the simple interest can be calculated on a principal P at an interest rate $R$ for time period $T$ as $\left( {\dfrac{{P \times R \times T}}{{100}}} \right)$. We will elaborate each option turn by turn to get to the final answer.

Complete step by step answer:
In the given question, Mr. Gupta has borrowed money on compound interest for two yearsWe need to calculate the amount to be repaid after two years. For calculating the amount after two years, we have to find the rate of interest and principal amount from the given statements.So, we will analyse the statements one by one and find the statements that are not necessary for calculation of the amount to be paid after two years. So, according to the first statement, the interest earned at the same amount in one year is $Rs\,600$.
Now, we get, $P{\left( {1 + \dfrac{R}{{100}}} \right)^1} - P = Rs600$
$ \Rightarrow \dfrac{{P \times R}}{{100}} = Rs600$
$ \Rightarrow P \times R = 60000$
So, we get a relation between rate of interest and principal amount from the first statement.
Now, according to the second statement, the simple interest earned at the same amount in one year is $Rs\,600$.

Now, we get, $\left( {\dfrac{{P \times R \times 1}}{{100}}} \right) = Rs600$
$ \Rightarrow \dfrac{{P \times R}}{{100}} = Rs600$
$ \Rightarrow P \times R = 60000$
So, we get a relation between rate of interest and principal amount from the second statement as well.
Now, according to the third statement, the simple interest earned at the same amount in one year is $Rs600$.
Now, we get, $\left( {\dfrac{{P \times R \times 1}}{{100}}} \right) = Rs600$
$ \Rightarrow \dfrac{{P \times R}}{{100}} = Rs600$
$ \Rightarrow P \times R = 60000$
So, we get a relation between rate of interest and principal amount from the second statement as well.

Now, according to the third statement, the amount borrowed is ten times the simple interest in two years.
Now, we get, $P = 10\left( {\dfrac{{P \times R \times 2}}{{100}}} \right)$
Cancelling the common factors in numerator and denominator, we get,
$ \Rightarrow P = \left( {\dfrac{{P \times R}}{5}} \right)$
Dividing both sides of the equation by P, we get,
 $ \Rightarrow R = 5$
So, the rate of interest is $5\% $. Hence, the third statement gives us the value of rate of interest. Now, on analyzing all the three statements, we realize that the third statement is necessary for the calculation of the amount to be paid after two years as it gives us the rate of interest.

Also, first and second statements provide us with the relations between principal amount and rate of interest. So, we can calculate the principal amount by substituting in the value of interest rate in any of the two relations. Hence, only one of the first and second statements is required for solving the problem. Therefore, either statement I or statement II is redundant in solving the question.

Hence, the option C is correct.

Note:Simple interest is very easy to calculate when we are given the principal amount, the time duration for which the loan is taken and the rate of interest charged by the institution which in this case is the bank. We must take care of the calculations to be sure of the final answer. We must remember that the time duration is not always equal to the number of time periods. The equality holds only when the compound interest is compounded annually.