Question

find simple interest​

Answer 1

Question :-

Ramesh lent out ₹ 5000 to Ram for 2 years at a certain rate of simple interest and lent out ₹ 600 to Shyam for 5 years at the same rate of interest. If he gets ₹ 455 in all as interest from both of them. Find the rate of interest.

$\large\underline{\sf{Solution-}}$

Case :- 1

Ramesh lent out ₹ 5000 to Ram for 2 years at a certain rate of simple interest.

Let assume that rate of interest be r % per annum.

So, we have

Principal, P = ₹ 5000

Time, n = 2 years

Rate of interest = r % per annum

We know,

Simple interest ( SI ) received on a certain sum of money of ₹ P invested at the rate of r % per annum for n years is given by

$\boxed{\sf{  \: \: SI \: = \: \frac{P \: \times \: r \: \times \: n}{100} \: \: }}$

So, on substituting the values, we get

$\rm \: SI_{1} \: = \: \dfrac{5000 \times r \times 2}{100}$

$\rm\implies \:\rm \: SI_{1} \: = \: 100r - - - (1)$

Case :- 2

Ramesh lent out ₹ 600 to Shyam for 5 years at the same rate of simple interest as in case 1.

So, we have

Principal, P = ₹ 600

Time, n = 5 years

Rate of interest = r % per annum

So,

$\rm \: SI_{2} \: = \: \dfrac{600 \times r \times 5}{100}$

$\rm\implies \:\rm \: SI_{2} \: = \: 30r - - - (2)$

Now, According to statement, he received ₹ 455 as interest from both of them.

$\rm \:SI_{1} + SI_{2} = 455$

$\rm \: 100r + 30r = 455$

$\rm \: 130r = 455$

$\rm\implies \:r \: = \: 3.5 \: \% \: per \: annum$

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Additional Information :-

Amount received on a a certain sum of money of ₹ P invested at the rate of r % per annum for n years is given by

$\boxed{\sf{  \: \: Amount \: = \: P \: \bigg[\dfrac{100 + rn}{100} \bigg] \: \: }}$

Also,

$\boxed{\sf{  \: \: P \: = \: \frac{SI \times 100}{r \times n} \: \: }}$

$\boxed{\sf{  \: \: r \: = \: \frac{SI \times 100}{P \times n} \: \: }}$

$\boxed{\sf{  \: \: n\: = \: \frac{SI \times 100}{P \times r} \: \: }}$

Answer 2

Part 1 of the question :-

$\sf \: Principal \:=\:₹\:5000 \\ \\ \sf \: Time\:=\:2\:years$

$\sf \color{red} \boxed{Simple\: Intrest\:=\: \frac{P\:\times\:R\:\times\:T}{100}}$

Applying the values,

$\sf Simple\: Intrest\:=\: \frac{5\cancel{000}\:\times\:R\:\times\:2}{1\cancel{00}}$

$\sf\implies\: Simple\:Intrest\:=\:100R \: \: \: \: \: \color{aqua} ( \color{aqua}\leadsto \: equation \: 1)$

Part 2 of the question :-

$\sf \: Principal\:=\:₹\:600 \\ \\ \sf \: Time\:=\:5\:years$

$\sf \: SI_2\:=\: \frac{P \: \times \: R \: \times \: T}{100}$

$\sf \: SI_2\:=\: \frac{6 \cancel{00} \: \times \: R \: \times \: 5}{1 \cancel{00}}$

$\implies \: SI_2\:=\:30R$

$\sf \: He \: received \: ₹ \: 455 \: as \: intrest \: fo r\: both \: of \: them \: (given).$

$\sf \: So \: putting \: the \: values \: of \: SI\:and\:SI_2\:and\: equating \:it\:by\:₹\:455.$

$\sf \implies \: 100r\:+\:30r\:=\:455 \\ \\ \sf \implies \:130r \: = \: 455 \\ \\ \sf \implies \:r \: = \frac{ \cancel{455}^{ \: \: 3.5} }{ \cancel{130}} \\ \\ \implies \: r \: = \: 3.5 \: \% \:$

$\sf \therefore \:Rate\:of\:Intrest\:=\:3.5\: \% \:or \: 3\: \frac{1}{2} \: \%\:.$

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