QUESTION

# A sum was put at simple interest at a certain rate for 5 years. Had it been put at 2% higher rate, it would have fetched Rs450 more. Find the sum.

Since, Simple interest = $\dfrac{{principle \times rate \times time}}{{100}}$
Simple interest at initial rate = $\dfrac{{\Pr \times 5}}{{100}}$
Simple interest at rate+2% = $\dfrac{{\operatorname{P} \left( {r + 2} \right)5}}{{100}}$
$\dfrac{{\operatorname{P} \left( {r + 2} \right)5}}{{100}} - \dfrac{{\Pr \times 5}}{{100}} = 450 \\ \Rightarrow \dfrac{{5\Pr + 10P - 5\Pr }}{{100}} = 450 \\ \Rightarrow P = \dfrac{{450 \times 100}}{{10}} = Rs4500 \\$