Question

Amit invested some part of \[35,000\] rupees at \[4\% \] and the rest at \[5\% \] interest for one year altogether her gain was \[Rs1530\], find out the amount she invested at the two different rates and write the answer in words.

Answer 1

Hint: In the given question, we have been given that a particular amount of money was invested. Some part of money was invested at one rate and the remaining at other. We have to find the respective amounts. To do that, we are going to use the formula of simple interest by assuming the separate amounts, put in the values and find the answer.

Formula Used:
We are going to use the formula of simple interest, which is,
\[A = \dfrac{{P \times R \times T}}{{100}}\]

Complete step by step solution:
The given amount is \[Rs35,000\].
Let the amount invested at \[4\% \] be \[x\]. Then, the amount invested at \[5\% \] is going to be \[35000 - x\].
Now, the gain at the given structure is \[Rs1,530\] and the given time is \[1\] year.
So, we have,
\[1530 = \dfrac{{x \times 4 \times 1}}{{100}} + \dfrac{{\left( {35000 - x} \right) \times 5 \times 1}}{{100}}\]
Multiplying both sides by \[100\], we have,
\[153000 = 4x + \left( {35000 - x} \right) \times 5\]
Opening the brackets and solving,
\[153000 = 4x + 175000 - 5x\]
Taking like terms on different sides,
\[175000 - 153000 = 5x - 4x\]
So, we have, \[x = 22000\].
Hence, the amount invested at \[4\% \] is \[Rs22000\] (Twenty Two Thousand Rupees) and the amount invested at \[5\% \] is \[Rs13000\] (Thirteen Thousand Rupees).

Note: In the given question, we were given a particular amount of money. It was broken into two and invested at different rates. We had to find the respective broken amounts. We did that by assuming the amounts and using the formula of simple interest. Then we just put in the values into the formula, simplified the result, and found our answer.