Answer

Verified

357.8k+ views

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.

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.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How many crores make 10 million class 7 maths CBSE

The 3 + 3 times 3 3 + 3 What is the right answer and class 8 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE