Question

Rs. 9000 becomes Rs. 27000 at simple interest in 10 years. Find the rate of interest per annum. Also find the
time period required to make the initial Principal amount into Rs.45000 with the same rate of interest

Answer 1

$\large \underline{ \underline { \text{Question:}}}$

• Rs. 9000 becomes Rs. 27000 at simple interest in 10 years. Find the rate of interest per annum.
• Also find the time period required to make the initial Principal amount into Rs.45000 with the same rate of interest.

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

Finding The Rate of Interest Per Annum,

Here,

• $\text{Amount} = Rs. \: 27000$
• $\text{Principal} = Rs. \: 9000$

And,

• $\text{Time} = 10 \: \text{years}$

As we know,

• $\boxed{ \text{Simple Interest} = \text{Amount} - \text{Principal }}$

Finding The Simple Interest,

$\implies \text{Simple Interest} = 27000 - 9000$

$\implies \text{Simple Interest} = Rs. \: 18000$

Here,

• $\text{Simple Interest} = Rs. \: 18000$

As we know,

• $\boxed{ \text{S.I} = \frac{ \text{Principal} \times \text{Rate} \times \text{Time}}{100}}$

Substituting the values and Finding the Rate,

$\implies 18000 = \frac{ 9000 \times \text{Rate} \times 10}{100}$

$\implies 18000 = 90 \times \text{Rate} \times 10$

$\implies 18000 = 900 \times \text{Rate}$

$\implies \text{Rate} = \frac{18000}{900}$

$\implies \text{Rate} = \frac{180}{9}$

$\implies \text{Rate} = 20\%$

Hence,

• The Rate of Simple Interest is 20% p.a.

Finding the Time Period,

Here,

• $\text{Principal} = Rs. \: 9000$
• $\text{Rate} = 20\%$

And,

• $\text{Amount} = Rs. \: 45000$

As we know,

• $\boxed{ \text{Simple Interest} = \text{Amount} - \text{Principal }}$

Finding the Simple Interest,

$\implies \text{Simple Interest} = 45000 - 9000$

$\implies \text{Simple Interest} = Rs.\:36000$

Here,

• $\text{Simple Interest} = Rs.\:36000$

As we know,

• $\boxed{ \text{S.I} = \frac{ \text{Principal} \times \text{Rate} \times \text{Time}}{100}}$

Substituting the values and Finding the Time Period,

$\implies 36000 = \frac{ 9000\times 20 \times \text{Time}}{100}$

$\implies 36000 = 90\times 20 \times \text{Time}$

$\implies 36000 = 1800 \times \text{Time}$

$\implies \text{Time} = \frac{36000}{1800}$

$\implies \text{Time} = \frac{360}{18}$

$\implies \text{Time} = 20 \: \text{years}$

Hence,

• The Time Period is 20 years.

$\\ \large \underline {\underline {\text{Required Answer:}}}$

• The Rate of Simple Interest is 20% p.a. In which, Rs. 9000 becomes Rs. 27000 at simple interest in 10 years.

• The Time Period is 20 years. In which, make the initial Principal amount into Rs.45000 with the same rate of interest.

Answer 2

Rate of Interest :-

Amount = ₹27000

Principal = ₹9000

Time = 10 years

Wkt:- S.I = A - P

Simple interest :-

= 27000-9000 = ₹18000

Now, S.I = P*R*T/100

18000 = 9000*Rate*10/100

18000 = 900*Rate

Rate = 18000/900

Rate = 20%

Time period :-

P = ₹9000

R = 20%

A = ₹45000

Now, S.I = A - P

S.I = 45000-9000

S.I = ₹36000

S.I = P*R*T/100

36000 = 9000*20*T/100

36000 = 1800*Time

T = 36000/1800

Time = 20 years

__________________________

• The Rate of Simple Interest is 20% p.a. In which, Rs. 9000 becomes Rs. 27000 at simple interest in 10 years.
• The Time Period is 20 years. In which, make the initial Principal amount into Rs.45000 with the same rate of interest.

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