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Given: Final amount ($A$) is \[Rs.{\text{ }}6655\]

Principal ($P$) is \[Rs.{\text{ }}5000\]

Compound interest rate ($r$) is \[10{\text{ }}\% \]

To find: Required time (in no. of years) to produce a given amount

To find this, there is a formula for finding the amount that will be produced after a certain time i.e, the amount produced will be the product of Principal with the one plus rate of compound interest per annum divided by 100 along with the power of no. of years (for which Principal will be compounded.)

The formula we need to apply here is

A = P${\left( {1 + \dfrac{{10}}{{100}}} \right)^t}$

Putting the values of A, P, r from the above question,

$6655$=\[{\text{ }}5000\] ${\left( {1 + \dfrac{{10}}{{100}}} \right)^t}$

$ \Rightarrow \dfrac{6655}{5000}=$ ${\left( {1 + \dfrac{{10}}{{100}}} \right)^t}$

By dividing both numerator & denominator by $5$

$ \Rightarrow $$\dfrac{{1331}}{{1000}}$= ${\left( {1 + \dfrac{1}{{10}}} \right)^t}$

Simplifying numerical part for covenience in comparision

$ \Rightarrow $${\left( {\dfrac{{11}}{{10}}} \right)^3}$ = ${\left( {\dfrac{{11}}{{10}}} \right)^t}$

Comparing both sides of the equation,

As the base of indices are same, by laws of indices powers also should be equal.

$ t=3$