Question

A sum of money after the end of 4 years at 5% p. A. Amounts rs. 2136. Find the time in which the same sum will double itself at the same rate.​

Answer 1

$\textbf{Given:}$

$\textsf{A sum of money after the end of 4 years at 5 percent}$

$\textsf{per annumAmounts Rs. 2136}$

$\textbf{To find:}$

$\textsf{The time in which the same sum will double itself at the same rate.​}$

$\textbf{Solution:}$

$\textbf{Simple interest formula:}$

$\boxed{\begin{minipage}{7cm} \\\mathsf{Simple\;interest=\dfrac{P\;n\;r}{100}}\\ \end{minipage}}$

$\textsf{when the sum gets doubled,}$

$\mathsf{Interest=P}$

$\mathsf{\dfrac{Pnr}{100}=P}$

$\mathsf{\dfrac{P{\times}n{\times}5}{100}=P}$

$\mathsf{\dfrac{P{\times}n}{20}=P}$

$\mathsf{\dfrac{n}{20}=1}$

$\implies\boxed{\mathsf{n=20\;years}}$

$\textbf{Answer:}$

$\textsf{The sum will take 20 years to become double}$

$\textbf{Find more:}$

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3.The simple intrest of a sum of Rs 4800 for 2 years is Rs 768 what will be the compound intrest on the same sum at the same rate and for the same period

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4.Compound interest on a certain sum of money at the rate of 5% becomes rupees 1537.50 in 2 years. Find the simple interest on same sum for same time at same rate interest.

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Answer 2

The amount is 1780 Rs.

The time in which the sum will double itself is 20 years

Step-by-step explanation:

Given:

A sum of money after 4 years at 5% per annum rate amounts to Rs. 2136

To find out:

The time in which the sum doubles at 5% per annum rate

Solution:

Let the sum be P

Rate of interest r = 5% p.a.

Period n = 4 years

Amount A = Rs. 2136

Therefore, Interest I = A - P

Using the simple interest formula

$I=\frac{nPr}{100}$

$A-P=\frac{nPr}{100}$

$\implies 2136-P=\frac{4\times P\times 5}{100}$

$\implies 2136-P=\frac{P}{5}$

$\implies P+\frac{P}{5}=2136$

$\implies \frac{6P}{5}=2136$

$\implies P=\frac{2136\times 5}{6}$

$\implies P=1780$ Rs.

Let the period in which the sum will double is n'

Then Interest accumulated = 2P - P = P

Thus,

$P=\frac{n'Pr}{100}$

$\implies n'=\frac{100}{r}$

$\implies n'=\frac{100}{5}$

$\implies n'=20$ years

Hope this answer is helpful.

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