Question

A person borrowed Rs.500 @ 3% per annum S.I and Rs.600 @\[4\dfrac{1}{2}\%\] per annum on the agreement that the whole sum will be returned only when the total interest becomes Rs.126. The number of years, after which the borrowed sum is be returned is:
\[\begin{align}
  & (\text{A) 2} \\
 & \text{(B) 3} \\
 & \text{(C) 4} \\
 & \text{(D) 5} \\
\end{align}\]

Answer 1

Hint: We know that if Rs. X is borrowed by a person at the interest of y%, then the amount of interest after one month is equal to \[\left( \dfrac{y}{100} \right)X\] . Now we will calculate the interest obtained for Rs.500 @ 3% per annum S.I for one year. And we will calculate the interest obtained for Rs.600 @ \[4\dfrac{1}{2}\%\] per annum S.I for one year. Now we will add money obtained by interests for one year. Let us assume that the person has to pay the interest for x years. Now the interest for x years is obtained in terms of x. Now we will equate this to Rs. 126. So, we will calculate the value of x. This value of x gives the number of years the person has to return the borrowed sum.

Complete step by step answer:
Before solving the question, we should know that as Rs. X is borrowed by a person at rate of interest of y%, then the amount of interest after one month is equal to \[\left( \dfrac{y}{100} \right)X\].
We are given that a person borrowed Rs.500 @ 3% per annum S.I.
So, the per annum interest that the person has to pay \[=\dfrac{3}{100}(500)=15\]
We were also given that a person also borrowed Rs.600 @\[4\dfrac{1}{2}\%\] per annum S.I.
So, the per annum interest that the person has to pay \[=\dfrac{\left( 4\dfrac{1}{2} \right)}{100}(600)=\dfrac{\left( \dfrac{9}{2} \right)}{100}(600)=\dfrac{9}{2}(6)=27\]
So, the total interest per annum to be paid by the person \[=15+27=42\]
Let us assume that the person has to pay this interest for x years. Then,
The total interest to be paid by the person for x years \[=42x\]
We were given that the interest for the sum is Rs.126. So, we get
\[\Rightarrow 42x=126\]
By using cross multiplication, we get
\[\begin{align}
  & \Rightarrow x=\dfrac{126}{42} \\
 & \Rightarrow x=3 \\
\end{align}\]
So, it is clear to us that the person took the interest for 3 years.
Hence, we can conclude that if a person borrowed Rs.500 @ 3% per annum S.I and Rs.600 @\[4\dfrac{1}{2}\%\] per annum on the agreement that the whole sum will be returned only when the total interest becomes Rs.126. Then the number of years, after which the borrowed sum is returned is equal to 3.

So, the correct answer is “Option B”.

Note: While solving this type of problems, calculation mistakes are generally possible. Students should be very careful while doing calculation. Small errors in calculation will give a wrong answer. We should be careful while converting the mixed fraction \[4\dfrac{1}{2}\] into a proper fraction. If a small mistake is done, the whole solution may go wrong. There will be several places where a student may undergo calculation mistakes. This should be avoided while solving the problem.