Question

In how much time simple interest on Rs.5000 at a rate of$ 12.5% be the same as the simple interest on Rs.6500 at the rate of 6.5% for 3 years?

Answer 1

Hint: To solve this question, firstly note down the information’s given in the question. We should have the concept of simple interest crystal clear so that it can be applied here. Find out the simple interest in the first case with an unknown term & then find the same for the second case. Compare them & solve for the unknown term that will be the ultimate answer.

Complete step by step solution:
We know that simple interest is the amount of money produced for keeping some Principal at a certain rate for a definite time. It is calculated by multiplying Principal, rate of interest per annum & no. of years for which it is kept.
So, in the first case –
Principal (p) $ = Rs.5000 = pRs.$
Let, time be $t$ years for which amount has been kept.
Rate $ = 12.5\% $$ = r\% $
We know, SI (Simple interest) $ = \dfrac{{p \times t \times r}}{{100}}$. So by putting the values of p & r here
$ = \dfrac{{5000 \times t \times 12.5}}{{100 \times 10}}$
$ = 625t$
Therefore, simple interest for first case is $Rs.625 \times t$.
Now, for $2nd$ case, now calculate simple interest on $Rs.6500$ at the rate of $6.5\% $ for $3$ years
Principal (p) $ = Rs.6500$
Time $\left( t \right) = 3years$
Rate $\left( r \right) = 6.5\% $
Therefore, simple interest $ = SI = \dfrac{{p \times t \times r}}{{100}}$
$ = \dfrac{{6500 \times 3 \times 6.5}}{{100 \times 10}}$
$ = \dfrac{{4225 \times 3}}{{10}}$
According to question, they are equal to each other i.e.,
SI for $1st$ year = SI for $2nd$ year.
$\therefore 625 \times t = \dfrac{{4225 \times 3}}{{10}}$
$ \Rightarrow t = \dfrac{{4225 \times 3}}{{10 \times 625}}$
$ = \dfrac{{169 \times 3}}{{10 \times 25}}$
$ = 2\dfrac{7}{{25}}$ years.

Therefore, required time is $2\dfrac{7}{{25}}$ years.

Note:
We need to have a concept of simple interest that what it is actually & how it is to be calculated. Read the question carefully to understand that for what information they have asked for. Do the calculation carefully to avoid silly mistakes instead of knowing the concept & procedure to do the sum. Don’t forget to give unit along with the magnitude because a no. without a unit (years here) is meaningless.