Answer

Verified

447.9k+ views

**Hint:**In this question we are given that certain sum of money amounts to a particular amount in some given time at simple interest.Use the formula of simple interest for amount $Rs.6300/-$ and consider it as equation 1 .Then apply simple interest formula again for amount $Rs.7875/ - $ and consider it as equation 2.Now divide both equations to get the value of rate of interest per annum.

**Formula used:**$Amount = P\left( {1 + \dfrac{{T \times R}}{{100}}} \right)$ where $P$ is principal amount, $R\% $ is rate of interest, $T$ is the time period.

**Complete step-by-step answer:**

According to the question we need to find the rate of interest i.e. simple interest.

So, we will use the formula for simple interest,

$Amount = P\left( {1 + \dfrac{{T \times R}}{{100}}} \right)\,\,\,\,\,\,\,\, \to (1)$ where $P$ is principal amount, $R\% $ is rate of interest, $T$ is the time period. We are given that the sum of money amounts to $Rs.6300/ - $in $2$ years. So let $Rs.\,P$ be the principal amount and $R\% $ be the rate of interest per annum. Now using (1),

$6300 = P\left( {1 + \dfrac{{2 \times R}}{{100}}} \right)\,\,\,\,\,\,\,\,\,\,\, \to (2)$

Also we are given that a sum of money amounts to $Rs.7875/ - $in $3$ years and $9$ months.

Now the time period is not in years,

Time period $ = $ $3$years and $9$ months

$ = 3\dfrac{9}{{12}} = \dfrac{{15}}{4}$years

Now using (1) we get,

$7375 = P\left( {1 + \dfrac{{15 \times R}}{{400}}} \right)\,\,\,\,\,\,\,\,\,\, \to (3)$

Now dividing (2) by (3) we get,

$

\dfrac{{6300}}{{7375}} = \dfrac{{P\left( {1 + \dfrac{{2 \times R}}{{100}}} \right)\,}}{{P\left( {1 + \dfrac{{15 \times R}}{{400}}} \right)\,}} \\

\dfrac{4}{5} = \dfrac{{(100 + 2R)400}}{{(400 + 15R)100}} \\

\dfrac{4}{5} = \dfrac{{(100 + 2R)4}}{{(400 + 15R)}} \\

400 + 15R = 500 + 10R \\

15R - 10R = 500 - 100 \\

5R = 400 \\

R = 20\% \\

$

So we get the rate of interest per annum equal to $20\% $.

**Note:**In this question we take time period in years and generally we make this type of mistakes by not converting time period in years.

Recently Updated Pages

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

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

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

Trending doubts

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

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

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How do you graph the function fx 4x class 9 maths 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