At what rate percent simple interest will a sum of money triples itself in 6 years?

Answer

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.

the given question is in how much time will a sum of money triples itself at 25% per annum right so let us assume let the sum of money aur which we can call it is principle bpxx2 we have assumed that the amount the principal amount is rupees X so they are saying at in how much time so we need to find value of time right we don't have value of time right now we have given that at rate of 25% so rate is given is 25% saying that it will triple itself write the amount we will get is amount will be triple which means 3 times of principle write three times of principle which means

3x surmount s3x so now we know that amount is Principal plus interest right so first of all we need to find value of interest value of interest can be determined as b into our into t upon hundred tried so value of P is principal amount is X into latest 25 into time is left city and upon 125 125 force so interest is X into TX Ti bi fore right sunao we know that amount is equal to principal plus interest value of amount is 3x right we have value of amount s3x principle as X and interest we have XT by so3 put it in negative sign so we're left with 3 x minus 6 is equals to x t by

3 x minus axis 3x 3x - 2 x = 2 x 3 by 4 write so now we have X Put It Down value of x to X by X equal to have to find value of time right so access cancelled so now we're left with two equal to 3 by 4 multiply 3 year so value of 22 and 24 which is it so in 8 years of time in 8 years of time the amount of the principal amount will XXXL right this is our required answer

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Solution

The correct option is D 50 %Given, time = 4 years. Let the sum invested be ₹ 100. So, the Amount received after 4 years = ₹ 300. We know that, Principal + Interest = Amount. Hence, Interest = Amount - Principal = ₹ (300-100) = ₹ 200. The Simple Interest earned on a sum of ₹ P for a period of T years at the rate of R% p.a S.I is given by P×R× T100. So, ₹ 200 = 100×R× 4100 Hence, R = 50%.

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