Question

In how many years Rs. \[{\text{150}}\] will produce the same interest at \[{{8\% }}\] p.a. as Rs. \[{\text{800}}\] produce in\[{\text{ 3}}\] years at \[{\text{4}}\dfrac{1}{2}\% \] p.a.?
A. \[6\]
B. \[8\]
C. \[9\]
D. \[12\]

Answer 1

Hint: Here, we are going to find the time period of which will produce the same amount of interest for the two data that are given above
In this we need to find the Simple interest for the data that given above
We can find the simple interest for the data which they have given
After that we will get the amount of interest
Now applying them on the formula of simple interest
And just we need to simplify them.
Finally, we will get the result that is the time period of which the amount will produce the same interest.

Formula used: \[{\text{SI}} = \dfrac{{{\text{Principal}} \times {\text{Time Period}} \times {\text{Rate Of Interest}}}}{{100}}\]

Complete step-by-step solution:
Here, the data which are given in the question
Principal\[ = \] \[800\], Rate of interest \[ = \] \[{\text{4}}\dfrac{1}{2}\% \] \[ = \] \[\dfrac{9}{2}\] , Time Period \[ = \] \[3\]years
By applying these data on the simple interest formula, we have
\[{\text{SI}} = \dfrac{{{\text{Principal}} \times {\text{Time Period}} \times {\text{Rate Of Interest}}}}{{100}}\]
Simple Interest \[{\text{ = }}\]\[800\]\[{{ \times }}\] \[\dfrac{9}{2}\]\[{{ \times }}\] \[\dfrac{3}{{100}}\] \[ = \] \[108\]
Here we got a result that the interest for the given data is \[108\]
Now, using the result that we got, we can apply them on formula to get time period of which we get the same interest
Principal \[{\text{ = 150}}\]
Simple Interest \[ = \] \[108\]
Rate of interest \[{{ = 8\% }}\]
\[{\text{SI}} = \dfrac{{{\text{Principal}} \times {\text{Time Period}} \times {\text{Rate Of Interest}}}}{{100}}\]
\[108 = \dfrac{{150 \times {\text{Time Period}} \times 8}}{{100}}\]
By bringing the values on one side and unknown on the other side we get,
Time Period \[{\text{ = }}\dfrac{{100 \times 108}}{{150 \times 8}}\]
Let us multiply the numerator and denominator term we get,
\[{\text{ = }}\dfrac{{10800}}{{1200}}\]
On cancelling the term we get,
\[{\text{ = }}\dfrac{{108}}{{12}}\]
On dividing we get the time Period \[ = 9\] years

\[\therefore \] The Time period which is required to get the same amount of interest is \[9\] years.

Note: Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments. By using the simple interest formula get the previous interest rate then add the given rate. Find simple interest with the new rate. Now we subtract both the total amount and we will get an increasing amount.