The problem states:

"The difference between simple interest on a certain sum of money for 2 years and 3 years at 10% per annum is ₹300. Find the sum."

Step-by-step solution:

Let the principal amount (the sum) be $P$.

The formula for simple interest (SI) is: $SI = \frac{P \times R \times T}{100}$ Where:

• $P$ is the principal amount.
• $R$ is the rate of interest (10% in this case).
• $T$ is the time in years.

Interest for 2 years:

$SI_2 = \frac{P \times 10 \times 2}{100} = \frac{P \times 20}{100} = 0.2P$

Interest for 3 years:

$SI_3 = \frac{P \times 10 \times 3}{100} = \frac{P \times 30}{100} = 0.3P$

Difference between the interests:

$SI_3 - SI_2 = 0.3P - 0.2P = 0.1P$

According to the problem, this difference is ₹300: $0.1P = 300$

Solving for $P$:

$P = \frac{300}{0.1} = 3000$

Final answer:

The sum is ₹3000.

Would you like more details or have any other questions about the solution?

Here are 5 related questions for practice:

1. What would be the sum if the rate of interest were 5% instead of 10%?
2. How much simple interest would be earned on ₹3000 at 10% in 5 years?
3. What is the difference between the interest for 1 year and 2 years at 10% on ₹3000?
4. How would the principal change if the difference in interest was ₹400 instead of ₹300?
5. How would the interest change if the principal was doubled but the time and rate remained the same?

Tip: The key in simple interest problems is that the interest grows linearly with time. This makes it easy to compare changes over different time periods.