Question

Two equal sums of money were invested, one at $4\% $ and other at $4\dfrac{1}{2}\% $ . At the end of 7 years, the simple interest received from the latter exceeded that received from the former by Rs.31.50. What was each sum?

Answer 1

Hint- In order to solve this question, we will assume the sum invested in the process as an unknown variable. Then we will make equations by the help of given statements and solve the equations in order to find the sum.

Complete step by step answer:
Let the sum invested be Rs. x.
Time = 7 years
Rates for both the investment = $4\% $ and $4\dfrac{1}{2}\% $ .
As we know that if the principal amount is P, rate of interest is R and time is T. Then the simple interest will be $\dfrac{{P \times R \times T}}{{100}}$
For case 1 let us find the simple interest.
$
  \because SI = \dfrac{{P \times R \times T}}{{100}} \\
   \Rightarrow S{I_1} = \dfrac{{x \times 4 \times 7}}{{100}} \\
   \Rightarrow S{I_1} = \dfrac{{28x}}{{100}}.........(1) \\
 $
For case 2 let us find the simple interest.
$
  \because SI = \dfrac{{P \times R \times T}}{{100}} \\
   \Rightarrow S{I_2} = \dfrac{{x \times 4\dfrac{1}{2} \times 7}}{{100}} = \dfrac{{x \times \dfrac{9}{2} \times 7}}{{100}} \\
   \Rightarrow S{I_2} = \dfrac{{63x}}{{200}}..........(2) \\
 $
As we know that the simple interest received from the latter exceeded that received from the former by Rs.31.50.
So $S{I_2} - S{I_1} = Rs.31.50$
Let us now substitute the values from equation (1) and equation (2) to find the value of x.
$
   \Rightarrow S{I_2} - S{I_1} = Rs.31.50 \\
   \Rightarrow \dfrac{{63x}}{{200}} - \dfrac{{28x}}{{100}} = 31.50 \\
 $
Now let us take LCM and solve further
$
   \Rightarrow \dfrac{{63x - 56x}}{{200}} = 31.50 \\
   \Rightarrow \dfrac{{7x}}{{200}} = 31.50 \\
   \Rightarrow 7x = 31.50 \times 200 \\
   \Rightarrow 7x = 6300 \\
   \Rightarrow x = \dfrac{{6300}}{7} \\
   \Rightarrow x = Rs.900 \\
 $
Hence, Rs. 900 was invested as sum in both the cases.

Note- Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments. In order to solve such questions students must deal with both the cases separately.