1. ₹6300 is divided into two parts in such a way that the simple interest on the first part at an annual rate of 10% for 6 years is equal to the simple interest on the second part at an annual rate of 15% for 3 years. Find the amounts of the two parts.

(a) ₹ 2700,₹3600 (b) ₹ 3000,₹ 3300 (c) ₹ 4000,₹ 2300 (d) ₹ 5000,₹ 1300

2. Divide ₹549 into two parts such that the interest on the first part at an annual rate of 7% for 6 years is equal to the interest on the second part at an annual rate of 10% for 8 years. Determine the two parts.

(a) ₹ 320,₹ 229 (b) ₹510,₹ 39 (c) ₹360, ₹ 189 (d) none of the above

3. 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

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. Aman borrowed ₹25,000 for 3 years, with annual compound interest rates of 4% for the first year, 5% for the second year, and 6% for the third year. What amount will Aman repay (including principal and interest) at the end of 3 years?

6. 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?

7. A man borrowed a certain amount of money at an annual compound interest rate of 5%. He repaid ₹3,150 at the end of the first year and ₹4,410 at the end of the second year to clear the loan. What was the amount he originally borrowed?

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

9. My uncle borrowed ₹40,000 for 3 years in such a way that the annual compound interest rates for the first, second, and third years were 2%, 3%, and 4% respectively. How much money will he repay (principal + interest) at the end of 3 years?

10. Rambabu divided his total money between two banks in such a way that he received equal interest from both banks after one year. The annual interest rates of the two banks are 4% and 5%, respectively. The amount of money deposited in the second bank is — of the amount deposited in the first bank.

(a) \(\frac{1}{2}\) part (b) \(\frac{1}{3}\) part (c) \(\frac{1}{6}\) part (d) twice

11. If the difference between the compound interest and simple interest on a certain amount for 3 years at an annual interest rate of 10% is ₹930, then calculate and write that principal amount.

12. What should be the annual compound interest rate for a certain amount of money to become 1.96 times that amount in 2 years?

13. Uday Babu lent a certain amount of money to one person at an annual simple interest rate of 4% for 4 years, and twice that amount to another person at an annual simple interest rate of 10% for the same duration. He received ₹960 more interest from the second person than from the first. Find the total amount of money Uday Babu lent.

14. Bimal Babu lent a certain amount of money to one person at an annual simple interest rate of 8% for 4 years, and twice that amount to another person at an annual simple interest rate of 10% for the same duration. Bimal Babu received ₹960 more interest from the second person than from the first. Find the total amount of money Bimal Babu lent.

15. 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.

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. If the interest is compounded every 6 months at an annual rate of 10%, then calculate the compound interest and the total amount on ₹1600 for \(1\cfrac{1}{2}\) years.

18. If the principal is \(p\) rupees and the annual compound interest rates for the first, second, and third years are \(r_1\%\), \(r_2\%\), and \(r_3\%\) respectively, then what will be the total compound amount after 3 years?

19. Here's the English translation of your sentence: Calculate the compound interest and the total amount on ₹2,400 for 1½ years at an annual compound interest rate of 10%, compounded semi-annually.

20. If the simple interest on a certain amount at an annual interest rate of 8% for 2 years is ₹850, then what will be the compound interest for the same period?

(a) ₹ 1684 (b) ₹984 (c) ₹ 884 (d) none of the above

21. If a certain amount of money grows to ₹12,100 in 3 years and ₹14,641 in 5 years at a compound interest rate, what is the annual interest rate?

(a) 10% (b) 15% (c) 5% (d) 12%

22. 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.

23. What is the compound amount for 10,000 rupees at an annual interest rate of 5% for \(2\cfrac{1}{2}\) years?

24. 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?

25. If interest is compounded every 6 months, then at an annual compound interest rate of 10%, what is the total compound amount and compound interest on 8000 rupees for \(1\frac{1}{2}\) years?

26. At an annual compound interest rate of 5%, if the compound interest on a certain sum of money for 2 years is ₹615, determine the principal amount.

27. In compound interest, if the interest rates for the first, second, and third years are \(r_1\%\), \(r_2\%\), and \(2r_3\%\) respectively, then the amount after 3 years on a principal of ₹\(P\) will be: \[ P\left(1 + \cfrac{r_1}{100}\right)\left(1 + \cfrac{r_2}{100}\right)\left(1 + \cfrac{r_3}{100}\right) \]

28. 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.

29. I have ₹5000. I deposited this amount in a bank at an annual compound interest rate of 8.5%. Write the calculation to determine the total amount (principal + interest) I will receive after 2 years.

30. Determine the compound amount for ₹5000 at an annual compound interest rate of 8% for 3 years.