How much time will it take for an amount of $Rs.450$ to yield $Rs.81$ as interest at $4.5\%$ per annum calculated at simple interest?

The correct option is B: $4$ years

Given: Principal, $P=Rs.450.$

Rate, $R=4.5\%$ per annum

Simple Interest, $S.I=Rs.81.$

Let the time taken be $t$ years. Then,

$S.I=\frac{P\times R\times t}{100}$

$\Rightarrow 81=\frac{450\times 4.5\times t}{100}$

$\Rightarrow t=\frac{100\times 81}{450\times 4.5}$

$\Rightarrow t=\frac{100\times 9}{45\times 5}$

$\Rightarrow t=\frac{100\times 1}{5\times 5}$

$\Rightarrow t=\frac{100}{25}=4$ years