Question

A sum of money at simple interest amounts to Rs. 815 in 3 years and to 854 in 4 years. The sum is:
A. Rs.650
B. Rs.690
C. Rs.698
D. Rs,700
E. Rs.715

Answer 1

Hint: In this problem, we need to find the amount of interest in 1 year. Then, find the amount of interest in 3 years and subtract it from 815. The amount of interest in 1 year is calculated by subtracting the amount in 3 years from the amount in 4 years.

Complete step by step answer:
The amount of interest in 1 year is calculated as shown below.
\[
  {\text{ Interest in 1 year}} = {\text{Amount in 4 year}} - {\text{Amount in 3 year}} \\
   \Rightarrow {\text{ Interest in 1 year}} = 854 - 815 \\
   \Rightarrow {\text{ Interest in 1 year}} = {\text{Rs}}.39 \\
\]
The amount of interest in 3 years is calculated as shown below.
\[
  {\text{ Interest in 3 years}} = 3\left( {{\text{Interest in 1 year}}} \right) \\
   \Rightarrow {\text{Interest in 3 years}} = 3\left( {39} \right) \\
   \Rightarrow {\text{Interest in 3 years}} = {\text{Rs}}.117 \\
\]
Now, the amount of money is calculated as shown below.
\[
  \,\,\,\,\,\,\,{\text{Sum of money}} = {\text{Amount in 3 years}} - {\text{interest in 3 years}} \\
   \Rightarrow {\text{Sum of money}} = 815 - 117 \\
   \Rightarrow {\text{Sum of money}} = {\text{Rs}}.698 \\
\]

So, the correct answer is “Option C”.

Note: In case of simple interest, amount of interest for 1 year can be obtained by subtracting the amount in 3 years from the amount in 4 years. We can solve this problem using a simple interest formula also. Form two equations in terms of interest rate and principle, and then solve both equations to find out the principle.