Question

In how many years does a certain sum amount to three times the principle at the rate of \[16\dfrac{2}{3}\%\]?
(A) \[12years\]
(B) \[8years\]
(C) \[4years\]
(D) \[18years\]

Answer 1

Hint: We are provided with the simple interest at the end of a time period to be three times in terms of principal amount at the rate of \[16\dfrac{2}{3}\%\]. In order to find the time period of this increase in the amount, we will substitute the given values in the formula of simple interest and solve for the time period. As the simple interest is expressed in terms of principal amount, so it gets cancelled out and solving further we get the value of time taken.

Complete step by step solution:
According to the given question, we have been given a sum which after an unknown period of time becomes three times the principle amount we had. And the rate given is \[16\dfrac{2}{3}\%\], so we have to find this unknown time frame after which the sum got thrice the principle amount.
We know the formula of simple interest, which is,
\[S.I=\dfrac{P\times R\times T}{100}\]------(1)
where P refers to the principal amount
R refers to the rate of interest
and T refers to the time period
according to the question given we have,
\[R=16\dfrac{2}{3}\%=\dfrac{50}{3}\%\]
\[S.I=3P\]
Substituting the values in the equation (1), we get,
\[S.I=\dfrac{P\times R\times T}{100}\]
\[\Rightarrow 3P=\dfrac{P\times R\times T}{100}\]
\[\Rightarrow 3P=\dfrac{P\times \left( \dfrac{50}{3} \right)\times T}{100}\]
\[\Rightarrow 3P=\dfrac{P\times 50\times T}{100\times 3}\]
We will cancel out P from the above expression as it occurs across either side of the equality. We get,
\[\Rightarrow 3\times 100\times 3=50\times T\]
Writing the expression in terms of T, we get,
\[\Rightarrow T=\dfrac{3\times 100\times 3}{50}\]
Solving further, we get,
\[\Rightarrow T=18yrs\]
So, it will take 18 years for the sum amount to be equal to three times the principle amount.

So, the correct answer is “Option D”.

Note: The interest added is not compound interest as in the question it was given that the sum at the end of a fixed time period rose to 3 times the principle amount. Compound interest adds interest not only on the principle amount but also on the interest added.