59. in what time at simple interest will a sum of money triples itself at 10%?

Last updated date: 28th Dec 2022

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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.

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Solution

The correct option is D20%2P=P×R×10100 ⇒R=20%

In how many years will a sum of money triple itself, at 20% per annum simple interest.

1. 6 years
2. 12 years
3. 10 years
4. 8 years

Answer (Detailed Solution Below)

Option 3 : 10 years

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Important Civilization in Rajasthan

15 Questions 15 Marks 10 Mins

Given:

Rate (R) = 20%

Formula used:

S.I. = (P × R × T)/100

Where, S.I. → Simple Interest

P → Principal

R → Rate 

T → Time 

Calculations:

Let the sum of money be  Rs. P.

So, A = 3P

And S.I. = A - P = 3P – P = 2P

Thus T = (100 × S.I.)/(P × R) 

⇒ T = (100 × 2P)/(P × 20) = 10 years

∴ The required time is 10 years.

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