Question

In how many years will \[Rs.150\] double itself at $4\% $ simple interest?

Answer 1

Hint: Here in this question we have principal and rate given so by using the amount which is twice of principal, from this we will get the amount and we also know $A = P(1 + TR/100)$ . So from this, we can now calculate the time required.

Formula used:
Amount,
$A = 2P$
And also, $A = P(1 + TR/100)$
Here,
$A$ , will be the amount.
$P$ , will be the principal.
$T$ , will be the time.
$R$ , will be the rate.

Complete step-by-step answer:
 First of all we will see the values given to us. So we have
Principal, $P = Rs.150$
And, rate, $R = 4\% $
Therefore, by using the amount formula, we have
$A = 2P$
On substituting the values, we get
$ \Rightarrow A = 2 \times Rs.150$
Now on solving the multiplication, we get
$ \Rightarrow A = Rs.300$
Now let us assume that the time will be $T$ years.
So, by using the amount formula again which is $A = P(1 + TR/100)$ . Therefore, on substituting the values, we get
$ \Rightarrow 300 = 150(1 + 4T/100)$
Now on solving the above equation, we get
$ \Rightarrow \dfrac{{300}}{{150}} = 1 + T/25$
On solving the division of LHS, we get
$ \Rightarrow 2 = 1 + T/25$
Mow on taking the constant term one side and solving the above equation, we get
$ \Rightarrow 1 = T/25$
Taking the denominator to the LHS side, so it will get multiplied and therefore, the time we get is
$ \Rightarrow T = 25$
Therefore, time is $25 years$ .


Note: This question can also be solved by using the simple interest formula, for the amount will be calculated the same as we had calculated but the only thing we will change is putting the values in the formula, which is given as $S.I = \dfrac{{P \times R \times T}}{{100}}$ of simple interest directly and then we can get the solution easily. Here, all the terms we already knew and $S.I$ , will be known to be as simple interest.