Question

A certain sum of money becomes three times itself in $20$ years at simple interest. In how many years does it become double of itself at the same rate?
(A) $8$ years
(B) $10$ years
(C) $12$ years
(D) $14$ years

Answer 1

Hint:Assume some variable for the initial sum and then frame a relationship using the above data in question. Use the formula $S.I. = \dfrac{{Principle \times Rate \times Time}}{{100}}$ and $Amount = Principle + S.I.$ to figure out the rate and then use the value to find the time.

Complete step-by-step answer:
Let us analyse the given data in the question first. For our ease, let us assume that the certain sum of money is ‘P’ that was invested initially.
So according to the question, after $20$ years the amount becomes $3 \times P$ and we have to find after how many years the amount will become $2 \times P$.
Now establish a relation using all the above information
$ \Rightarrow $ Amount$ = $ Principal Sum$ + $Interest$ = P + \dfrac{{P \times Rate \times Time}}{{100}}$.........$(1)$
$ \Rightarrow $ $3 \times P = P + \dfrac{{P \times Rate \times 20}}{{100}}$
Dividing both right and left-hand sides with ‘P’
$ \Rightarrow 3 = 1 + \dfrac{{Rate \times 20}}{{100}}$
From the above-obtained equation we can easily figure out the Rate of the Simple interest, by further solving it:
$ \Rightarrow 3 - 1 = \dfrac{{Rate \times 20}}{{100}} \Rightarrow Rate = 2 \times 5 = 10\% $
Similarly, we can put all the given information in the above equation for an amount of $2 \times P$
After substituting values in $(1)$, we get:
$ \Rightarrow 2 \times P = P + \dfrac{{P \times 10 \times Time}}{{100}}$
Now, dividing again both sides with ‘P’, it changes our equation to:
$ \Rightarrow 2 = 1 + \dfrac{{10 \times Time}}{{100}}$
This equation can be further solved for the value of ‘Time’
$ \Rightarrow 2 - 1 = \dfrac{{10 \times Time}}{{100}} \Rightarrow Time = \dfrac{{1 \times 100}}{{10}} = 10$ years

So, the correct answer is “Option B”.

Note:It’s always better to understand it properly and write down the given information first. An alternative approach can be when you use the formula of simple interest to calculate interest separately then add it to the principal amount. Assuming a variable for unknowns will always make it easier to execute.