At what rate percent per annum simple interest will a sum of money triple itself in 25 years?

Correct Answer - Option 1 : 8%

Formula used 

SI = (P × R × T)/100

SI = Simple interest

P = Principal

R = Rate

T = Time

Calculation

Let principal be 100Rs

⇒After 25 years principal = 300

⇒ SI = 300 - 100 = Rs.200

⇒ 200 = (100 × r × 25)/100

⇒ r = 8 %

∴ At 8 percent per annum simple interest, a sum of money triple itself in 25 yr

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.

At what rate percent per annum simple interest, will a sum of money triple itself in 25 yr ?duplicate options found. English Question 1 options 1,3

1. 8%
2. 9%
3. 10%
4. 12%

Answer (Detailed Solution Below)

Option 1 : 8%

Free

ACC 124 GMAT Paper (Held in Feb 2021)

150 Questions 300 Marks 180 Mins

Formula used 

SI = (P × R × T)/100

SI = Simple interest

P = Principal

R = Rate

T = Time

Calculation

Let principal be 100Rs

⇒After 25 years principal = 300

⇒ SI = 300 - 100 = Rs.200

⇒ 200 = (100 × r × 25)/100

⇒ r = 8 %

∴ At 8 percent per annum simple interest, a sum of money triple itself in 25 yr

Last updated on Sep 29, 2022

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Simple interest

Aptitude

1. At what rate percent per annum simple interest , will a sum of money triple itself in 25 year?

1. 1. 8%
   2. 5%
   3. 6%
   4. 12 %

Correct Option: A

Let principal amount = P
As amount =3P, T=25 yr
∴ SI=3P-P=2P
∴ Rate R = (100 x SI)/(P x T)
where, SI= Simple Interest T = Time
= (100 x 2P)/(P x 25)=8%

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