Solution : Let T years be the required time period. <br> Given that, <br> Amount `(A)=3 xx ` Principal (P) <br> `therefore P(1+(TR)/(100))=3P` <br> `implies 1+(12T)/(100)=3 implies T=(200)/(12)=16(2)/(3)` years <br> Hence, required time period`=16(2)/(3)` years.
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Solution
Let sum of money be P=100
Interest per annum =10%
amount = 2× 100 = 200
simple interest = 200 - 100 = 100
Since,
SI=PTR100
⇒T=100×SIPR
=100×100100×10
∴t=10 years.
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Solution
The formula for simple interest calculation is -
I = P*R*T/100
Where I is interest
P is principal amount
R is rate of interest
T is time in Years.
Now you want to triple the money. That means I = 2P
Hence 2P = P*R*T/100
2*100 = 15*T
Hence T = 200/15 = 13.33Y or 13Y and 4 months.
So the answer for your question is 13Y and 4 months.
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.