Question

At what rate percent per year will a sum double itself in $6\dfrac{1}{4}$years?

Answer 1

Hint: We have to find the percentage of rate at which the sum doubles itself in $6\dfrac{1}{4}$years. So, we will assume the initial amount as ‘x’. And we will also use a simple interest formula. By substituting all the required values in the formula as simplifying the equation, we will get the answer.

Complete step-by-step answer:
Assume the principal amount is $x$.
The principal amount doubles itself. So, it will become $2x$.
Money from interest will be $ = 2x - x$$ \Rightarrow x$
Assume the rate of interest as ‘r’.
Now, we will use a simple interest formula. But first we will discuss it. Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. Simple interest is calculated with the following formula
$S.I. = P \times R \times T$where P = Principal, R = Rate of Interest in % per annum, and T = Time usually calculated as the number of years. The rate of interest is in percentage r % and is to be written as $\dfrac{r}{{100}}$.
$S.I. = P \times R \times T$
Substituting the values in formula.
$x = \dfrac{{x \times r \times 6\dfrac{1}{4}}}{{100}}$
$100 = r \times \dfrac{{25}}{4}$
$400 = r \times 25$
$r = \dfrac{{400}}{{25}}$
$r = 16\% $
So, the rate is 16%.
So, the correct answer is “Option B”.

Note: Whenever this type of question is asked we will find the interest on principal amount by subtracting principal amount from the money after the number of years given in the question and then we will assume rate of interest to be r and then apply, Simple Interest formula and find the required value of rate of interest.