Question

A sum of Rs6000 amounts to Rs6900 in 3 years.What will it amountto if the rate of interest is increased by 2%​

Answer 1

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 :-

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

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

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 ,

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

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,

$\longrightarrow{\tt{900 = \dfrac{6000 \times 3 \times x }{100}}}$

$\longrightarrow{\tt{ 900 = 60 \times 3 \times x }}$

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

Interchange the terms on both sides

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

$\longrightarrow{\tt{ x = \dfrac{900}{180}}}$

$\longrightarrow{\tt{ x = 5 \% }}$

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 ,

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

So,

$\longrightarrow{\tt{ S.I. = \dfrac{ 6000 \times 3 \times 7}{100}}}$

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

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

Hence,

Interest = Rs. 1260

Now ,

Using the formula in order to find the amount

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

So,

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

$\rm{Amount = Rs. 7260 }$

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

Answer 2

$\sf\large\underline{Given:}$

• $\sf\large{Principal=Rs.6000}$
• $\sf\large{Amount=Rs.6900}$
• $\sf\large{Time=3\: year's}$

$\sf\large\underline{To\:Find:}$

• $\rm{The\: amount\: after\: increasing\: rate\:by\:2\%}$

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

• At 1st calculate rate of interest than calculate the the amount after increasing rate by 2%

$\rm{\implies SI=A-P}$

$\rm{\implies SI=6900-6000}$

$\rm{\implies SI=Rs.900}$

• Now calculate rate of interest here]

$\rm\green{\implies R=\dfrac{SI*100}{P*T}}$

$\rm{\implies R=\dfrac{900\times100}{6000\times3}}$

$\rm{\implies R=\dfrac{90000}{18000}}$

$\rm\red{\implies R=5\%}$

• By solving we get rate of interest is equal to 5% than we have to add 2%more with the original rate which is obtained by calculating.

$\sf\large\underline{We\: have\:,now:}$

• $\rm{Principal=Rs.6000}$
• $\rm{Rate=7\%}$
• $\rm{Time=3\: year's}$
• $\rm{Amount=?}$

$\sf\large\underline{Formula\: used:}$

$\rm\purple{\implies SI=\dfrac{P*T*R}{100}}$

$\rm{\implies SI=\dfrac{6000\times3\times7}{100}}$

$\rm{\implies SI=60\times3\times7}$

$\rm\red{\implies SI=Rs.1260}$

• Now calculate amount here]

$\rm{\implies A=P+SI}$

$\rm{\implies A=6000+1260}$

$\rm\purple{\implies A=Rs.7260}$

$\sf\large\underline{Hence,:}$

$\rm{\implies The\: amount\: after\: increasing\: rate=Rs.7260}$