Answer
Verified
469.5k+ views
Hint: Simple interest is interest calculated on the principal portion of a loan or the original contribution to a saving account. The formula for the simple interest is $S.I. = \dfrac{{P \times R \times T}}{{100}}$. We are going to use the term Amount $A$ in the solution and it stands for sum of simple interest and the principal. It is the amount to which the borrower has to pay after a particular time.
Complete step by step solution:Simple Interest = $S.I.$ (in Rupees)
Amount = $A$ (in Rupees)
Principal =$P$ (in Rupees)
Time = $T$ (in years)
Rate = $R$ (in percentage per annum)
Main goal of the question is to find the time in which the principal will triple to itself. For that we should focus and simplify the given condition.
As given in the question,
In $10$ years principal $P$ becomes $2P$.
In $10$ years,
$A = 2 \times P$
Since Amount $A$ is considered as the sum of principal and the simple interest after $n$ years.
Therefore,
$ \Rightarrow P + S.I. = 2 \times P$
$ \Rightarrow 2P - P = S.I.$
$ \Rightarrow P = S.I.$
As we know the formula for simple interest is $S.I. = \dfrac{{P \times R \times T}}{{100}}$ . On substituting the formula,
$ \Rightarrow P = \dfrac{{P \times R \times T}}{{100}}$
Since it is given that $T = 10$ years.
$ \Rightarrow P = \dfrac{{P \times R \times 10}}{{100}}$
\[ \Rightarrow P = \dfrac{{P \times R}}{{10}}\]
$ \Rightarrow 10 \times P = P \times R$
$ \Rightarrow \dfrac{{10 \times P}}{P} = R$
$ \Rightarrow 10 = R$
Now, by simplifying the given condition we have the rate of interest as $R = 10\% $ per annum.
The time required to triple the principal (say $t$ ) can be found by the formula of Amount and simple interest.
$A = P + S.I.$
$ \Rightarrow 3 \times P = P + S.I.$ [According to question]
$ \Rightarrow 3 \times P - P = S.I.$
$ \Rightarrow 2P = S.I.$
$ \Rightarrow 2 \times P = \dfrac{{P \times R \times t}}{{100}}$
$ \Rightarrow 2 \times P \times 100 = P \times R \times t$
$ \Rightarrow \dfrac{{200 \times P}}{P} = R \times t$
$ \Rightarrow 200 = 10 \times t$
$ \Rightarrow t = 20$
Hence, the time required to triple the principal is $t = 20$ years.
Note: Generally the interest is of two types either simple or compounded. Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period.
Complete step by step solution:Simple Interest = $S.I.$ (in Rupees)
Amount = $A$ (in Rupees)
Principal =$P$ (in Rupees)
Time = $T$ (in years)
Rate = $R$ (in percentage per annum)
Main goal of the question is to find the time in which the principal will triple to itself. For that we should focus and simplify the given condition.
As given in the question,
In $10$ years principal $P$ becomes $2P$.
In $10$ years,
$A = 2 \times P$
Since Amount $A$ is considered as the sum of principal and the simple interest after $n$ years.
Therefore,
$ \Rightarrow P + S.I. = 2 \times P$
$ \Rightarrow 2P - P = S.I.$
$ \Rightarrow P = S.I.$
As we know the formula for simple interest is $S.I. = \dfrac{{P \times R \times T}}{{100}}$ . On substituting the formula,
$ \Rightarrow P = \dfrac{{P \times R \times T}}{{100}}$
Since it is given that $T = 10$ years.
$ \Rightarrow P = \dfrac{{P \times R \times 10}}{{100}}$
\[ \Rightarrow P = \dfrac{{P \times R}}{{10}}\]
$ \Rightarrow 10 \times P = P \times R$
$ \Rightarrow \dfrac{{10 \times P}}{P} = R$
$ \Rightarrow 10 = R$
Now, by simplifying the given condition we have the rate of interest as $R = 10\% $ per annum.
The time required to triple the principal (say $t$ ) can be found by the formula of Amount and simple interest.
$A = P + S.I.$
$ \Rightarrow 3 \times P = P + S.I.$ [According to question]
$ \Rightarrow 3 \times P - P = S.I.$
$ \Rightarrow 2P = S.I.$
$ \Rightarrow 2 \times P = \dfrac{{P \times R \times t}}{{100}}$
$ \Rightarrow 2 \times P \times 100 = P \times R \times t$
$ \Rightarrow \dfrac{{200 \times P}}{P} = R \times t$
$ \Rightarrow 200 = 10 \times t$
$ \Rightarrow t = 20$
Hence, the time required to triple the principal is $t = 20$ years.
Note: Generally the interest is of two types either simple or compounded. Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period.
Recently Updated Pages
10 Examples of Evaporation in Daily Life with Explanations
10 Examples of Diffusion in Everyday Life
1 g of dry green algae absorb 47 times 10 3 moles of class 11 chemistry CBSE
If the coordinates of the points A B and C be 443 23 class 10 maths JEE_Main
If the mean of the set of numbers x1x2xn is bar x then class 10 maths JEE_Main
What is the meaning of celestial class 10 social science CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In the tincture of iodine which is solute and solv class 11 chemistry CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE