Question

The Principal amount is Rs. 9540, the SI is Rs. 1908, and the rate is \[8\% \] p.a. Find the time and amount.

Answer 1

Hint:
Here, we need to find the time period and the amount. First, we will use the formula for simple interest and use the given information to find the time period. Then, we will use the formula for finding the amount. The amount is the sum of the principal amount and the interest.
Formula used: We will use the formula:
The simple interest is given by \[S.I. = \dfrac{{P \times R \times T}}{{100}}\], where \[P\] is the principal amount, \[R\] is the rate of interest, and \[T\] is the time period.
The amount is the sum of the principal amount and the interest. It is given by the formula \[A = P + S.I.\], where \[P\] is the principal amount and \[S.I.\] is the simple interest.

Complete step by step solution:
We will use the formula for simple interest to find the time and the formula for amount to find the amount.
Substituting \[P = {\rm{Rs}}{\rm{. }}9540\], \[S.I. = {\rm{Rs}}{\rm{. }}1908\], and \[R = 8\] in the formula \[S.I. = \dfrac{{P \times R \times T}}{{100}}\], we get
\[ \Rightarrow 1908 = \dfrac{{9540 \times 8 \times T}}{{100}}\]
This is a linear equation in one variable in terms of \[T\].
Now, we will simplify this equation to find the value of \[T\], and hence, the time period (in years).
Multiplying both sides by 100, we get
\[ \Rightarrow 1908 \times 100 = \dfrac{{9540 \times 8 \times T}}{{100}} \times 100\]
Thus, we get
\[ \Rightarrow 190800 = 9540 \times 8 \times T\]
Multiplying 9540 by 8, we get
\[ \Rightarrow 190800 = 76320 \times T\]
Dividing both sides of the equation by 76320, we get
\[ \Rightarrow \dfrac{{190800}}{{76320}} = \dfrac{{76320 \times T}}{{76320}}\]
Therefore, we get
\[ \Rightarrow T = \dfrac{5}{2} = 2.5\] years
\[\therefore \] We get the time period as \[2.5\] years, or 2 years 6 months.
Now, we will find the amount.
The amount is the sum of the principal amount and the interest.
It is given by the formula \[A = P + S.I.\], where \[P\] is the principal amount and \[S.I.\] is the simple interest.
Substituting \[P = {\rm{Rs}}{\rm{. }}9540\] and \[S.I. = {\rm{Rs}}{\rm{. }}1908\] in the formula, we get
\[ \Rightarrow A = {\rm{Rs}}{\rm{. }}9540 + {\rm{Rs}}{\rm{. }}1908\]
Adding 9540 and 1908, we get the amount as
\[ \Rightarrow A = {\rm{Rs}}{\rm{. }}11,448\]

\[\therefore \] The amount is Rs. 11,448.

Note:
We have formed a linear equation in one variable in terms of \[T\] using the given information and the formula for simple interest. A linear equation in one variable is an equation that can be written in the form \[ax + b = 0\], where \[a\] is not equal to 0, and \[a\] and \[b\] are real numbers. For example,
\[x - 100 = 0\] and \[100x - 566 = 0\] are linear equations in one variable \[x\].