Ram earns an interest of 600 over two years on a simple interest basis. On a…

Step-by-Step Solution

To find the rate of interest when the simple interest and compound interest for two years are known, we can follow this logical approach:

1. Analyze Simple Interest (SI):

   • SI for 2 years = 600.

   • Since simple interest is the same for each year, the SI for 1 year = 600 / 2 = 300.

2. Analyze Compound Interest (CI):

   • CI for 2 years = 630.

   • For the first year, SI and CI are identical. So, the interest for the first year is 300.

   • The interest for the second year in a compound interest setup is the interest on the principal plus the interest on the first year's interest.

   • CI for 2nd year = Total CI - CI for 1st year = 630 - 300 = 330.

3. Calculate the Interest on Interest:

   • The extra amount earned in CI compared to SI for the second year is the "interest on interest."

   • Extra interest = CI for 2nd year - SI for 1 year = 330 - 300 = 30.

   • This Rs. 30 is the interest earned on the Rs. 300 interest from the first year.

4. Find the Rate of Interest (R):

   • Using the formula: Interest = (Principal * Rate * Time) / 100

   • Here, the "Principal" for this calculation is the first year's interest (300), the "Interest" is 30, and Time is 1 year.

   • 30 = (300 * R * 1) / 100

   • 30 = 3 * R

   • R = 10%.