Question

Find the time Period for P= Rs 8000, R= 5%, S.I= Rs 400
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Answer 1

Time - Simple Interest

Simple Interest is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

But in this question, we have been asked to calculate the time period, which can be calculate only with the formula of simple interest.

The basic formula of Simple Interest is as follows:

$\implies SI = \dfrac{P \times R \times T}{100}$

Where, P denotes Principal Amount, R denotes Rate of Interest and T denotes Time Period.

According to the given question, we've been given that,

• Simple interest, SI = Rs. 400
• Principal amount, P = Rs. 8000
• Rate of interest, R = 5%
• Time period, T = ?

By using the simple interest formula and substituting all the given values, we get:

$\implies 400 = \dfrac{80\cancel{00} \times 5 \times T}{1\cancel{00}} \\ \\ \implies 400 = 80 \times 5 \times T \\ \\ \implies 400 = 400 \times T \\ \\ \implies T = \cancel{\dfrac{400}{400}} \\ \\ \implies \boxed{\bf{T = 1}}$

Hence, the time period is 1 years.

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IMPORTANT FORMULAE

Simple interest SI on a certain sum of money of Rs P invested at the rate of R% per annum for T years is given by,

$\implies \boxed{\rm{SI = \dfrac{P \times R \times T}{100}}}$

Simple interest SI on a certain sum of money of Rs P invested at the rate of R% per month for n months is given by,

$\implies \boxed{\rm{SI = \dfrac{P \times R \times n}{12 \times 100}}}$

Simple interest SI on a certain sum of money of Rs P invested at the rate of R% per day (non-leap year) for d days is given by,

$\implies \boxed{\rm{SI = \dfrac{P \times R \times d}{365 \times 100}}}$

Answer 2

As per data given in the question,

We have to determine the value of "Time period", when an amount of Rs. 8000 gives an interest pf Rs. 400 at the rate of 5%.

As we know that,

The formula of Simple Interest is  

$\implies SI = \dfrac{P \times R \times T}{100}$

Where, P = Principal Amount,

R = Rate of Interest

and T = Time Period.

So, from the given data,

We have,

Simple interest, SI = Rs. 400

Principal amount, P = Rs. 8000

Rate of interest, R = 5%

Time period, T = ?

So, using the above mentioned formula,

We will get that,

$\implies 400 = \dfrac{80\cancel{00} \times 5 \times T}{1\cancel{00}} \\ \\ \implies 400 = 80 \times 5 \times T \\ \\ \implies 400 = 400 \times T \\ \\ \implies T = \cancel{\dfrac{400}{400}} \\ \\ \implies \boxed{\bf{T = 1}}$

Hence, the value of time period will be 1 years.