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
Last updated date: 30th Mar 2023
•
Total views: 307.8k
•
Views today: 4.84k
Answer
307.8k+ 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.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
