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At what rate a sum doubles itself in 8 year 4 months.
Given: A sum doubles itself in 8 year 4 months.
To find: Here we have to find the rate of interest at which a sum doubles itself in 8 year 4 months.
Solution:
Let the actual amount be = $a$
Now, this sum is doubled in 8 year 4 months:
Amount after 8 years 4 months = $2a$
Simple interest paid in 8 years 4 months:
SI = Amount after 8 years 4 months $-$ Actual amount
SI = $2a\ -\ a\ =\ a$
8 years 4 months = $\frac{25}{3}$ years
Also,
$SI\ =\ \frac{P\ \times \ R\ \times \ T}{100}$
$a\ =\ \frac{a\ \times \ R\ \times \ 25}{100\ \times\ 3}$
$a\ =\ \frac{a\ \times \ R}{4\ \times\ 3}$
$a\ =\ \frac{a\ \times \ R}{12}$
$\frac{12a}{a} =\ R$
$\mathbf{R\ =\ 12\%}$
So, rate of interest at which a sum doubles itself in 8 year 4 months is 12%.
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