Question

a sum of 6000rs amounts to 6900rs in 3 years . what will it amount to if the rate of interest is increased by 2%​

Answer 1

Step-by-step explanation:

Answer :-

Given :-

First case :-

Principal amount = Rs. 6000

Amount = Rs. 6900

Time = 3 years

Second case :-

Rate of interest increased by 2 %

Required to find :-

Rate of interest ( in the 1st case )

Amount (2nd case )

Formulae used :-

\large{\leadsto{\boxed{\rm{ Simple \; Interest = \dfrac{PTR }{100}}}}}⇝SimpleInterest=100PTR

\large{\leadsto{\boxed{\rm{ Amount = Principal + Interest }}}}⇝Amount=Principal+Interest

Solution :-

Consider the 1st case ;

Given that :-

Principal amount = Rs. 6000

Amount = Rs. 6900

Time = 3 years

He asked us to find the rate of interest .

In order to find the rate of interest we should find the interest

As we know that,

Amount = principal + Interest

So,

Interest = Amount - principal

Substitute the required values

Interest = 6900 - 6000

Interest = Rs. 900

Hence

Using the formula ,

\large{\leadsto{\boxed{\rm{ Simple \; Interest = \dfrac{PTR }{100}}}}}⇝SimpleInterest=100PTR

Here,

P = principal

T = Time

R = Rate of interest

However,

Let the rate of interest be " x "

Substitute the value

Here,

Simple Interest = Rs. 900

So,

\longrightarrow{\tt{900 = \dfrac{6000 \times 3 \times x }{100}}}⟶900=1006000×3×x

\longrightarrow{\tt{ 900 = 60 \times 3 \times x }}⟶900=60×3×x

\longrightarrow{\tt{900 = 180x }}⟶900=180x

Interchange the terms on both sides

\Rightarrow{\tt{ 180x = 900 }}⇒180x=900

\longrightarrow{\tt{ x = \dfrac{900}{180}}}⟶x=180900

\longrightarrow{\tt{ x = 5 \% }}⟶x=5%

Hence,

Rate of interest ( % ) = x = 5 %

So,

Now consider the 2nd case .

In this case we can use some values which is given in the First case should be used expect rate of interest , amount .

Because,

He mentioned that :-

If the rate of interest is increased by 2%

So,

The values are;

Principal = Rs. 6,000

Rate of interest = 5% + 2% = 7%

Time = 3 years

Using the formula ,

\large{\leadsto{\boxed{\rm{ Simple \; Interest = \dfrac{PTR }{100}}}}}⇝SimpleInterest=100PTR

So,

\longrightarrow{\tt{ S.I. = \dfrac{ 6000 \times 3 \times 7}{100}}}⟶S.I.=1006000×3×7

\longrightarrow{\tt{ S.I. = 60 \times 3 \times 7 }}⟶S.I.=60×3×7

\longrightarrow{\tt{ S.I. = Rs. \; 1260}}⟶S.I.=Rs.1260

Hence,

Interest = Rs. 1260

Now ,

Using the formula in order to find the amount

\large{\leadsto{\boxed{\rm{ Amount = Principal + Interest }}}}⇝Amount=Principal+Interest

So,

\rm{Amount = Rs. \; 6000 + Rs. \; 1260 }Amount=Rs.6000+Rs.1260

\rm{Amount = Rs. 7260 }Amount=Rs.7260

\large{\leadsto{\boxed{\tt{\therefore{Amount = Rs. \; 7260 }}}}}⇝∴Amount=Rs.7260