Given:
- A sum was put at simple interest at a certain rate for 5 years.
- Had it been put at 5% higher rate, it would have fetched Rs. 500 more.

To find: The sum

Solution:
Let the sum be x and the rate of interest be y.

According to the question,
Simple Interest (SI) for the given sum and rate = (x*y*5)/100
Simple Interest (SI) for 5% higher rate = (x*(y+5)*5)/100

As per the question, the difference between the two interests is Rs. 500.
So,

(x*(y+5)*5)/100 - (x*y*5)/100 = 500
=> xy/100 = 1000
=> xy = 100000

Therefore, the sum (x) can be calculated using the above equation as we know the value of xy.

Let's assume y = 5, then
x*5 = 100000
x = 20000/5
x = 4000

So, the sum is Rs. 4000.

Now, let's verify if the given conditions are satisfied.

SI for 5 years at 5% rate on Rs. 4000 = (4000*5*5)/100 = Rs. 1000
SI for 5 years at 10% rate on Rs. 4000 = (4000*10*5)/100 = Rs. 2000
The difference between the two interests is Rs. 2000 - Rs. 1000 = Rs. 1000

But, as per the question, the difference between the two interests should be Rs. 500. This means that the rate assumed above (y = 5) is higher than the actual rate.

Let's assume y = 4, then
x*4 = 100000
x = 25000

So, the sum is Rs. 25000.

Now, let's verify if the given conditions are satisfied.

SI for 5 years at 4% rate on Rs. 25000 = (25000*4*5)/100 = Rs. 5000
SI for 5 years at 9% rate on Rs. 25000 = (25000*9*5)/100 = Rs. 11250
The difference between the two interests is Rs. 11250 - Rs. 5000 = Rs. 6250

But, as per the question, the difference between the two interests should be Rs. 500. This means that the rate assumed above (y = 4) is higher than the actual rate.

Let's assume y = 2, then
x*2 = 100000
x = 50000

So, the sum is Rs. 50000.

Now, let's verify if the given conditions are satisfied.

SI for 5 years at 2% rate on Rs. 50000 = (50000*2*5)/100 = Rs. 5000
SI for 5 years at 7% rate on Rs. 50000 = (50000*7*5)/100 = Rs. 17500
The difference between the two interests is Rs. 17500 - Rs. 5000 = Rs. 12500

But, as per the