How many years will a principal at 8% pa simple interest becomes three times of the principal?

Simple interest

Aptitude

1. A certain sum of money becomes three times of itself in 20 years at simple interest. In how many years does it become double of itself at the same rate of simple interest ?
   

1. 1. 8 years
      
   2. 10 years
      
   3. 12 years
      
   4. 14 years

Correct Option: B

Case-I
Let the principal be P
Amount = 3P
∴ Interest = 2P
Time = 20 years

⇒ R = 10%
Case-II
SI = P
Principle = P
Rate = 10
Time = ?

∴ T = 10 years.
Second method to solve this question :

R% = 10%

T = 10 years

A sum invested on simple interest becomes triple itself in 16 years. Then the rate of interest is?

Answer

Verified

Hint: We will assume the sum invested as x rupees. We have been given that it becomes triple after 3 years which means it becomes 3 x. Now, we know that the final amount = principal amount + simple interest. So, we will find the simple interest from that and using the formula, $\text{simple interest}=\dfrac{\text{principal amount}\times \text{time}\times \text{rate}}{100}$, we will find the rate of interest.

Complete step-by-step answer:
We are given the time period as 16 years and that the sum becomes triple after 16 years. So, we will first assume the sum invested as Rs. x. We have been given that after 16 years, it becomes triple, so,
Final amount = $3\times x=3x$.
Now, we know that the final amount is the summation of the principal amount and simple interest,
Final amount = principal amount + simple interest, which can be written as,
3 x = x + simple interest, so we get the simple interest as = 3 x - x = 2 x.
Now, we have the principal amount, time and the simple interest, so we will find the rate using the formula, $\text{simple interest}=\dfrac{\text{principal amount}\times \text{time}\times \text{rate}}{100}$. So, by substituting the values of the parameters we get,
$\begin{align}
  & \dfrac{2x}{1}=\dfrac{x\times 16\times rate}{100} \\
 & \Rightarrow \dfrac{2}{1}=\dfrac{16\times rate}{100} \\
\end{align}$
On cross-multiplying, we get,
$\begin{align}
  & rate=\dfrac{2\times 100}{16} \\
 & \Rightarrow rate=12.5\% \\
\end{align}$
Hence, we get the rate of interest as 12.5 %.

Note: There is a possibility that the students think that the simple interest becomes triple of the principal amount, that is simple interest is 3 x. So, in further calculations for finding the rate of interest, they will end up with, $rate=\dfrac{3\times 100}{16}\Rightarrow 18.75\%$. But students should read the question carefully to understand that the sum becomes triple, which means the principal amount becomes triple after 16 years.

interview question in how many years will a certain sum becomes three times itself at 25% per annum under the simple interest so here in the given question the initial principal amount becomes 3 times at the rate of the 25% and then we have to find in how many years so here we first consider let the principal amount let the principal amount and then here it is denoted by capital P that one is equal 200 X and then Soya the final amount let it be denoted by capital A that will be equal to hear it is given it becomes three times so here it will be 3 into the get X which is the principal so here we get 300 X and then rupees so here the simple interest the simple interest simple

interest that will be equals to hear that will be close to the amount - principal amount so here it will be amount - here it is principal for the principal amount so kya we get is equals to 300 X - 100 x so here we get is equals to 200x and then rupees and it is given that the state here let it be noted by capital are that one is given and that what is equal to 25 % per annum so here it is 25% for and then it is and I'm so here we find out we have to find out the time which is it so here we use the formula of the simple interest here according to which year the simple hair simple interest we know the formula for that one is equal to p into our into it and then divided by 100 rupees the principal are is the rate and easy

time now we simply put the value so here the simple interest is this one which is 200x so here it is 200x that one is equal to your principal we have considered to be 100x so here it is 100 x into our rate that one is given to be 25 into which we have to find out and then divided by 100 Sohail this hundred cancel this one and here we get 200 X is equals to X into 25 into it so here we get the value of t is equals to 200 X and then divided by X into 25 Sohail sex cancel this one and then this 25 cancel this 200 so here we get it so here is equals to 8 or we can write it to be time that one is equals to 8 and then it is years in the given question in the given question option B is the right

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