A person invested ₹4,500 at 5% per annum and ₹5,500 at 8% per annum simple interest. Both investments were for 4 years. The amount obtained at the lower interest rate is what percent (rounded off to the nearest integer) of the amount obtained at the higher interest rate?

To solve this problem, we need to calculate the amounts obtained from both investments and then find the percentage of one amount relative to the other.

### Step 1: Calculate the simple interest from each investment
The formula for simple interest is:

\[
\text{Simple Interest (SI)} = \frac{P \times R \times T}{100}
\]

where:
- \(P\) is the principal amount,
- \(R\) is the rate of interest per annum, and
- \(T\) is the time in years.

#### For the ₹4,500 investment at 5% per annum:
\[
SI_1 = \frac{4500 \times 5 \times 4}{100} = \frac{90,000}{100} = ₹900
\]
The total amount obtained (Principal + Interest) is:
\[
A_1 = 4500 + 900 = ₹5400
\]

#### For the ₹5,500 investment at 8% per annum:
\[
SI_2 = \frac{5500 \times 8 \times 4}{100} = \frac{176,000}{100} = ₹1760
\]
The total amount obtained (Principal + Interest) is:
\[
A_2 = 5500 + 1760 = ₹7260
\]

### Step 2: Calculate the percentage
We are asked to find what percent the amount obtained at the lower interest rate (₹5400) is of the amount obtained at the higher interest rate (₹7260). This can be calculated as:

\[
\text{Percentage} = \frac{A_1}{A_2} \times 100 = \frac{5400}{7260} \times 100
\]

Let's compute this.

\[
\text{Percentage} \approx \frac{5400}{7260} \times 100 \approx 74.34\%
\]

### Step 3: Rounding off
Rounding off 74.34% to the nearest integer gives:

\[
\boxed{74\%}
\]

Thus, the amount obtained at the lower interest rate is approximately 74% of the amount obtained at the higher interest rate.

Would you like further details or have any questions?

### Related Questions:
1. What is the difference in interest earned between the two investments?
2. How would the result change if the investment periods were different?
3. What would be the total amount if both investments were made at the same interest rate?
4. How much additional interest would be earned if the ₹4,500 were invested at 8% instead?
5. What would the total amount be if the ₹5,500 were invested at 5% instead?

### Tip:
To quickly calculate simple interest, remember the formula \(\frac{P \times R \times T}{100}\), which gives you the interest directly without having to do multiple steps.

Learn how to compare simple interest returns from investments of ₹4,500 at 5% and ₹5,500 at 8%, both over 4 years. The detailed solution shows how to calculate simple interest and determine the percentage comparison between the two amounts. Perfect for students in Grades 8-10.

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