Question

A sum of money triples itself in \[15\] years \[6\] months. In how many years would it double itself?
A. \[6\] years \[3\] months
B. \[7\] years \[9\] months
C. \[8\] years \[3\] months
D. \[9\] years \[6\] months

Answer 1

Hint: To solve this question, we need to apply the basic formula of simple interest which is \[S.I. = \dfrac{{PTR}}{{100}}\] . In the question, we are given the time, so first we calculate the rate using principal amount and simple interest and then use this calculated rate to solve time for the second part.

Complete step-by-step answer:
In the question, it is given that a sum of money triples itself in \[15\] years \[6\] months
Therefore, let the sum be \[x\] then, simple interest \[S.I.\] will be \[2x\] .
Time required to triple the money is given as \[15\] years \[6\] months \[ = 15\dfrac{1}{2} = \dfrac{{31}}{2}\] years
Now, Simple Interest \[S.I. = \dfrac{{PTR}}{{100}}\]
Putting the values in above formula of simple interest, we get
\[2x = \dfrac{{x.\dfrac{{31}}{2}.R}}{{100}}\]
Or, \[R = \dfrac{{400}}{{31}}\% \]
Now, to calculate in how many years it becomes double,
So, it will now give \[x\] interest on the sum of \[x\] .
So, sum be \[x\] then, simple interest \[S.I.\] will be \[x\] .
Now, Simple Interest \[S.I. = \dfrac{{PTR}}{{100}}\]
Putting the values in above formula of simple interest, we get
\[x = \dfrac{{x.T.\dfrac{{400}}{{31}}}}{{100}}\]
Or, \[T = \dfrac{{31}}{4}\]
\[T = 7\dfrac{3}{4}\] years
Or, the time it takes to double is \[7\] years \[9\] months.

So, the correct answer is “Option B”.

Note: Remember the formula of simple interest. Simple interest is calculated by multiplying the interest rate by the principal amount and the time period which is generally in years. The \[S.I.\] formula is given as: \[S.I. = \dfrac{{PTR}}{{100}}\]