The simple interest on a sum of money will be Rs. 600 after 10 years. If the principal is trebled after 5 years. What will be the total interest at the end of tenth year?a)Rs. 600b)Rs. 900c)Rs. 1,200d)Rs. 1,000Correct answer is option 'C'. Can you explain this answer?

Question

Answer

Total Interest Calculation
To determine the total interest at the end of the tenth year, we need to analyze the situation step by step.
Initial Simple Interest Calculation
- Given that the simple interest accrued after 10 years is Rs. 600.
- This means that the interest earned annually (I) can be calculated as:
I for 10 years = Rs. 600
Therefore, I per year = Rs. 600 / 10 = Rs. 60
Principal Trebling After 5 Years
- Let’s denote the initial principal amount as P.
- For the first 5 years, the interest is calculated on the initial principal P:
Interest for first 5 years = 5 * Rs. 60 = Rs. 300
- After 5 years, the principal is trebled:
New principal = 3P
Interest Calculation for the Next 5 Years
- For the next 5 years, the interest is calculated on the new principal (3P):
Interest for next 5 years = 5 * Rs. 60 (interest rate remains the same) = Rs. 300
Total Interest at the End of 10 Years
- Now, we sum the interest earned over the 10 years:
Total Interest = Interest for first 5 years + Interest for next 5 years
Total Interest = Rs. 300 + Rs. 300 = Rs. 600
- However, we need to factor in the increased principal for the last 5 years.
Final Total Interest Calculation
- The interest for the last 5 years based on the trebled principal would actually be:
New interest = 5 * Rs. 60 (initial interest) + 5 * Rs. 60 (on new principal) = Rs. 600 + Rs. 600 = Rs. 1,200
Thus, the total interest at the end of the tenth year is Rs. 1,200. Therefore, the correct answer is option 'C'.

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