1. A man left ₹28,000 for his 13-year-old son and 15-year-old daughter with the instruction that, at the age of 18, the amount each receives — including simple interest at an annual rate of 10% — should be equal. Determine the amount allocated to each child.

2. If the simple interest and compound interest on a certain principal for 2 years are ₹8400 and ₹8652 respectively, then determine the principal and the annual rate of interest.

3. My aunt wants to will 56,000 INR between her two sons, aged 13 and 15, in such a way that when they turn 18, the total amount received (principal + interest) for each son will be equal, given a 10% annual simple interest rate. Determine the amount allocated for each son in the will.

4. Bimal Kaku deposited 56,000 INR in a bank for his two sons, aged 13 and 15 years, in such a way that when they turn 18, the simple interest earned at an annual rate of 10% on each deposit equals the respective principal amount. Determine how much he deposited in each son's name.

5. At an annual interest rate of 4%, the difference between the simple interest and compound interest on a principal amount for 2 years is 40 rupees. Determine the principal amount.

6. At the same annual percentage interest rate, the simple interest and compound interest on a principal amount become equal in _____ years (interest period: 1 year).

7. My aunt wants to will ₹56,000 between her two sons, aged 13 and 15, in such a way that by the time each turns 18, the total amount (principal + interest) received by both sons is equal. The interest is calculated at an annual simple interest rate of 10%. Determine how much should be allotted to each son in the will.

8. For a fixed amount of money at a fixed annual interest rate, the amount of compound interest and simple interest after 1 year will be equal.

9. At an annual percentage rate of interest, the simple interest and compound interest on a principal amount are equal after —— years.

10. A farmer deposited some money in the village post office. After 4 years, he found that the total amount including interest had become ₹434. He calculated that the interest he received was \(\frac{6}{25}\) of his principal amount. Find how much money he had originally deposited and what annual rate of simple interest the post office gave.

11. The simple interest for 2 years and the compound interest for 1 year (with annual compounding) on the same principal at the same rate are ₹800 and ₹820 respectively. Find the principal and the rate of interest.

12. What should be the annual rate of simple interest (in percent) so that the interest on a sum of money for 10 years becomes \(\frac{2}{5}\) of the total amount (principal + interest)?

13. For a fixed amount of money, at a fixed annual rate of interest, the compound interest and simple interest will be equal in -- years.

14. Mr. Amal bequeaths ₹56,000 in his will for his two sons aged 13 and 15 in such a way that, when they each turn 18, the simple interest earned at an annual rate of 10% will be equal to the principal for each. What will be the allocated amount for each son in the will?

15. If the difference between the compound interest and the simple interest on a certain sum of money for 2 years at an annual interest rate of 9% is ₹129.60, then find the principal amount.

16. If the difference between the compound interest and simple interest on a certain principal for 2 years at an annual rate of 5% is ₹25, then what is the amount of the principal?

17. Divide ₹1098 into two parts such that the principal plus interest on the first part at an annual rate of 5% for 9 years equals the principal plus interest on the second part at an annual rate of 8% for 2 years. Determine the two parts.

(a) ₹ 488 ₹ 610 (b) ₹1000 ₹ 98 (c) ₹ 900 ₹ 198 (d) none of the above

18. Determine the principal amount for which the difference between the simple interest and compound interest for 2 years at an annual rate of 4% is 40 rupees.

19. Determine the principal amount for which the difference between the simple interest and compound interest for 2 years at an annual rate of 4% is 80 rupees.

20. If the simple interest and compound interest for 2 years on a certain principal are ₹840 and ₹869.40 respectively, determine the principal amount and annual interest rate.

21. Anil Babu wants to allocate ₹56,000 between his two sons, aged 13 and 15, such that when they turn 18, the simple interest earned at an annual rate of 10% is equal to their respective principal amounts. Determine the amount allocated to each son in the will.

22. In how many years will the amounts of simple interest and compound interest be equal for the same principal at the same annual interest rate?

(a) 3 years (b) 2 years (c) 1 years (d) \(\frac{1}{2}\)

23. If the simple interest for 1 year on a certain principal amount is 500 rupees and the compound interest for 2 years is 1020 rupees, determine the principal amount and the annual simple interest rate.

24. At the same interest rate, the simple interest on a certain amount for 3 years is ₹1200, and the compound interest for 2 years is ₹832. Determine the interest rate and the principal amount.

25. At the same annual interest rate, the compound interest and simple interest on a principal amount will be equal.

(a) 1 years (b) 2 years (c) 3 years (d) 4 years

26. If the difference between the compound interest and simple interest on a certain sum for 3 years at an annual rate of 10% is 930 rupees, then what is the principal amount?

27. Determine the principal and the annual simple interest rate if a sum of money amounts to ₹7100 in 7 years and ₹6200 in 4 years at the same annual rate of simple interest.

28. Rahmat Chacha borrowed ₹240000 from a bank at an annual simple interest rate of 12% to build a house. One year after borrowing, he started renting out the house for ₹5200 per month. Calculate and determine after how many years from borrowing he will be able to repay the bank loan along with interest using the rental income.

29. Determine the annual simple interest rate (percentage) at which the interest on a certain amount over 10 years becomes \(\frac{2}{5}\) of the total amount (principal + interest).

30. Chhanda Devi borrowed some money for 2 years at an annual compound interest rate of 8%. If the compound interest amounts to ₹2496, determine how much money she borrowed.