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.

Answer 1

Hint- In this particular type of question we need to use the formula of simple interest and subtract the initial simple interest from the simple interest at 2% higher rate. Then we need to equate the result with Rs450 to get the desired sum.

Complete step-by-step answer:
Let the initial rate be r, principle be P and time = 5years (given)
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% = $\dfrac{{\operatorname{P} \left( {r + 2} \right)5}}{{100}}$
According to the question,
$
  \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 \\
$

Note- Remember to recall the formula of simple interest while solving these types of questions. Note that the time period and the principle remained the same in both cases which is the reason we get only one variable (P) at last. Had it been the question of compound interest the procedure of solving this question would have been quite different.