Answer
Verified
Hint: To solve the problem, we should know the definition of annual simple interest. We have,
Simple Interest (I) = $\dfrac{P\times R\times t}{100}$
Where, P= principal amount
R = simple interest annual rate
t = time period of the annual simple interest
Here, we have R = 10% and have to calculate t for the sum of the money (that is P) to double.
Complete step-by-step answer:
In this question, we are left with two unknowns, P and t. However, we also have an additional
condition. This condition tells that within the required time (which we have to calculate), the sum of money doubles itself. Thus, if originally, we had principal amount as P, finally, this amount would become 2P. Thus, simple interest (I) becomes 2P-P = P. Since, simple interest is basically the amount accumulated over the total principal amount. Further, for simplification, we can write,
$\dfrac{R}{100}=\dfrac{10}{100}=0.1$
Thus, we have,
I=$\dfrac{P\times R\times t}{100}$
Since, I
= P (as calculated above), we have,
P = $\dfrac{P\times R\times t}{100}$
We can cancel P from both sides. Thus, we have,
1=$\dfrac{R\times t}{100}$
Plugging in the known values, we have,
1= 0.1$\times $t
Since, $\dfrac{R}{100}$=0.1
Now,
t=10 years
Hence, it will take 10 years for the sum of money to double itself with the rate of 10% per annum simple interest.
Note: While solving questions related to principal interest, it is important to keep in mind that simple interest calculated from the formula, Simple Interest (I) = $\dfrac{P\times R\times t}{100}$ , doesn’t represent the total amount of money. In fact, the total amount is the sum of Principal amount (P) and simple interest. Thus, in this case, when money was doubled, the total amount was 2P and simple interest was P.
Given that, the sum of money triples itself in 20 years
∴ P + I = 3P
∴ I = 2P
and T = 20 years
Now simple interest I = `"PRT"/100`
∴ 2P = `("P" xx "R" xx 20)/100`
∴ R = 10
∴ Rate of interest = 10% per annum
The time period is to be calculated for the condition that the sum doubles itself i.e. for the condition
P + I = 2P
i.e. I = P
i.e. `("P" xx "R" xx "T")/100 = "P"`
∴ `(10 xx "T")/100 = 1`
∴ T = 10
∴ The sum will become double of itself in 10 years.
- 20%
- 17%
- 22%
- 15%
Answer (Detailed Solution Below)
Option 1 : 20%
Formula for Simple Interest -
\(SI = \frac{{P \times R \times T}}{{100}}\)
Where,
P = Principal
R = Rate of interest
T = Time period
Let the required rate of interest be X.
According to the question, SI must be equal to 2 × P in order to make the final sum two times the original principal amount after 5 year.
\(\therefore {\rm{P}} = {\rm{}}\frac{{{\rm{P}} \times {\rm{X}} \times 5}}{{100}}\)
⇒ X = 20%
∴ Required rate of interest is of 20%.
Stay updated with the Quantitative Aptitude questions & answers with Testbook. Know more about Interest and ace the concept of Simple Interest.
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Ifa sum of money double itself...
Updated On: 27-06-2022
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`4%``8%``5%``10%`
Answer : C
Answer
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