Question

In $ 4 $ years, ₹ $ 6000 $ amounts to ₹ $ 10000 $ . In what time will ₹ $ 500 $ amount to ₹ $ 700 $ at the same rate ?

Answer 1

Hint: The person must be getting some interest for the amount he has deposited. Use the formula of simple interest to find the rate of interest with which his amount changed. Then use the same rate of interest to find out how long it would take to receive ₹ 700 from ₹ 500.

Complete step-by-step answer:
Let us explain the question by taking an example.
Let us say that A deposited ₹ 6000 into some bank.
After 4 years he received ₹ $ 10000 $
To calculate the interest, he received, we will use the formula
 $ S.I = \dfrac{{P \times R \times T}}{{100}} $
Where,
SI is simple interest
P is the principle amount that was deposited
R is the rate of interest he received on the deposit
T is the time period for which he had his money invested.
The total interest he received at the end 4 years would be equal to the difference between the final amount he received and the initial amount he invested
 $ = 10000 - 6000 $
 $ = $ ₹ $ 4000 $
We need to calculate the rate of interest. For that, substitute the given information in the formula of simple interest. We get
According to the formula,
 $ S.I = \dfrac{{P \times R \times T}}{{100}} $
 $ \Rightarrow 4000 = \dfrac{{6000 \times R \times 4}}{{100}} $
By rearranging the above equation, we get
 $ R = \dfrac{{4000 \times 100}}{{6000 \times 4}} $
 $ \Rightarrow R = \dfrac{{50}}{3}\% $
Now, let us say he deposited ₹ 500 into the same bank at the same rate of interest. He expects to receive ₹ 700 as a return of his investments.
That means, he expects to receive ₹ 200 as interest.
As, Simple interest= $ A - P $
 $ = 700 - 500 $
 $ = 200 $
So, we would again use the formula of simple interest and substitute the given information in it.
 $ S.I = \dfrac{{P \times R \times T}}{{100}} $
 $ \Rightarrow 200 = \dfrac{{500 \times \dfrac{{50}}{3} \times T}}{{100}} $
By rearranging it, we get
 $ T = \dfrac{{200 \times 100 \times 3}}{{500 \times 50}} $
First cancel out the zeros from the numerator and denominator,
 $ T = \dfrac{{2 \times 10 \times 3}}{{5 \times 5}} $
Now simplifying it further, we get
 $ T = \dfrac{{2 \times 2 \times 3}}{5} $
 $ = \dfrac{{12}}{5} $
 $ \Rightarrow T = 2.4 $
Thus, he would need $ 2.4 $ years to receive ₹ 700 after depositing ₹ 500 at the rate of interest of $ \dfrac{{50}}{3}\% $

Note: In this question, it was not given whether the interest was a simple interest or a compound interest. So we could choose to solve it using simple interest. But it is not always necessary. Read the question carefully to know if the question is of simple interest or compound interest. From this question, you learn that when you get a question with some example, like in this question, you got an example of ₹ 6000 increasing to ₹ 10000. Then such a condition is always given to find some unknown quantity that is going to be used to solve the asked question. Always keep that in mind and use the given examples to find that unknown variable that you need.