Two equal sums of money were lent at simple interest at $11\% $p.a. for $3\dfrac{1}{2}$ years and $4\dfrac{1}{2}$ years respectively. If the difference in interest for two periods was $Rs.412.50$, find the sum.
A)Rs.3250
B)Rs.3500
C)Rs.3750
D)Rs.4250
Answer
363.6k+ views
Hint: Use simple interest formula to find simple interest -$1$ and simple interest-$2$ with given respective years of time period.
Simple interest =$\dfrac{{P \times T \times R}}{{100}}$
Complete step-by-step answer:
Here we need to find simple interests for the given years of time period.
According to data given let us find individual simple interest for given years of time period.
Let the each sum of money be $Rs.X$
Required data for simple interest-$1$
Principle =$Rs.X$
Rate = $11\% $p.a.
Time =$4\dfrac{1}{2}$ years = $4.5$years
Simple interest = $\dfrac{{P \times T \times R}}{{100}}$
Then,
Simple interest - $1$ ($S.{I_1}$) = $\dfrac{{X \times 11 \times 4.5}}{{100}}$
Required data for simple interest -$2$
Principle =$Rs.X$
Rate = $11\% $p.a.
Time = $3\dfrac{1}{2}$ years = $3.5$ years
Simple interest = $\dfrac{{P \times T \times R}}{{100}}$
Then,
Simple interest - $2$($S.{I_2}$) = $\dfrac{{X \times 11 \times 3.5}}{{100}}$
Given, difference in interest for two periods = $Rs.412.50$
Difference = $S.{I_1}$ - $S.{I_2}$
$412.50$ = $\dfrac{{X \times 11 \times 4.5}}{{100}}$ - $\dfrac{{X \times 11 \times 3.5}}{{100}}$
On simplification, we get
$
\Rightarrow 99X - 77X = 412.50 \times 200 \\
\Rightarrow 22X = 82500 \\
\Rightarrow X = \dfrac{{82500}}{{22}} \\
\Rightarrow X = 3750 \\
$
As we consider that the each sum of money as = $Rs.X$
Hence the value of each sum of money is $Rs.3750$
Option C is the correct answer.
NOTE: Here we have to find the simple interest individually for given periods. As we know that simple interest for a given time period will be different. And after finding simple interest-1 and simple interest-2, we have to find the difference between them.
Simple interest =$\dfrac{{P \times T \times R}}{{100}}$
Complete step-by-step answer:
Here we need to find simple interests for the given years of time period.
According to data given let us find individual simple interest for given years of time period.
Let the each sum of money be $Rs.X$
Required data for simple interest-$1$
Principle =$Rs.X$
Rate = $11\% $p.a.
Time =$4\dfrac{1}{2}$ years = $4.5$years
Simple interest = $\dfrac{{P \times T \times R}}{{100}}$
Then,
Simple interest - $1$ ($S.{I_1}$) = $\dfrac{{X \times 11 \times 4.5}}{{100}}$
Required data for simple interest -$2$
Principle =$Rs.X$
Rate = $11\% $p.a.
Time = $3\dfrac{1}{2}$ years = $3.5$ years
Simple interest = $\dfrac{{P \times T \times R}}{{100}}$
Then,
Simple interest - $2$($S.{I_2}$) = $\dfrac{{X \times 11 \times 3.5}}{{100}}$
Given, difference in interest for two periods = $Rs.412.50$
Difference = $S.{I_1}$ - $S.{I_2}$
$412.50$ = $\dfrac{{X \times 11 \times 4.5}}{{100}}$ - $\dfrac{{X \times 11 \times 3.5}}{{100}}$
On simplification, we get
$
\Rightarrow 99X - 77X = 412.50 \times 200 \\
\Rightarrow 22X = 82500 \\
\Rightarrow X = \dfrac{{82500}}{{22}} \\
\Rightarrow X = 3750 \\
$
As we consider that the each sum of money as = $Rs.X$
Hence the value of each sum of money is $Rs.3750$
Option C is the correct answer.
NOTE: Here we have to find the simple interest individually for given periods. As we know that simple interest for a given time period will be different. And after finding simple interest-1 and simple interest-2, we have to find the difference between them.
Last updated date: 01st Oct 2023
•
Total views: 363.6k
•
Views today: 3.63k
Recently Updated Pages
What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Why are resources distributed unequally over the e class 7 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Briefly mention the contribution of TH Morgan in g class 12 biology CBSE

What is the past tense of read class 10 english CBSE
