Question

how many years will it take for rupees 54000 to double at a simple interest rate of 8%?
answer should come 12.5 years..​

Answer 1

Required answer:–

Given:–

• R = 8%

• P = Rs. 54000

To find:–

• Time (n) taken to double amount

Assumptions:–

• Let amount be 2P

Where,

• R = Rate

• P = Principal

• n = Time

Formulas used:–

• Amount = Principal×Rate×Time / 100 + P

Step by step explaination:–

Calculating the amount and putting values...

That is,

2P = (54000 × N × R) / 100+P

2P-P = 54000×N×8 / 100

P = 540 × N × 8

Now putting the value of Principal...

That is,

54000 = 540 × N × 8

N = 54000 / 540×8

N = 12.5

Answer:–

Time (years) taken is 12.5 years

Extra information:–

★ The money borrowed is called the Principal, the extra money paid for using lender's money is called the interest and the total money, paid to the lender at the end of the specified period is called the amount.

______________________________

Note: When we say, interest it always means Simple Interest.

Answer 2

$\begin{gathered}\begin{gathered}\bf \: Given \:  - \begin{cases} &\sf{Principal = Rs \: 54000 } \\ &\sf{Amount = Rs \: 108000}\\ &\sf{Rate = 8 \: \% \: per \: annum} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To \: find \:  - \begin{cases} &\sf{time \: period}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

Given

• Principal, P = Rs 54, 000

• Amount, A = Rs 1, 20, 000

• Rate of interest, R = 8 % per annum

• Let time taken be 'T' years.

We know,

$\bigstar \: \: \boxed{ \pink{ \bf \: Interest \: = \: Amount \: - \: Principal}}$

$\rm :  \implies \:Interest \: = \: 120000 - 54000$

$\pink{\rm :  \implies \:Interest \: = \: Rs \: 54000}$

Now,

Using formula of Simple interest, we have

$\boxed{ \pink{{\sf{\star \: \: Simple \: interest \: = \: \dfrac{P \times R \times T}{100}}}}}$

where,

• P denotes Principal

• R denotes Rate

• T denotes Time

So,

$\rm :  \implies \:54000 = \dfrac{54000 \times 8 \times \: T }{100}$

$\rm :  \implies \:T \: = \: \dfrac{100}{8}$

$\rm :  \implies \:T \: = \: 12.5 \: years$

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