1. 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.

2. If the interest on a certain amount of money at an annual rate of 5% for 8 years is ₹246 more than the interest at an annual rate of 7% for 4 years, what is the principal amount?

(a) ₹ 5020 (b) ₹ 2000 (c) ₹ 2050 (d) ₹ 2005

3. In compound interest, if an amount becomes \(\cfrac{27}{8}\) times the principal in 3 years, what will be the annual rate of interest? Let me know if you'd like the full solution as well—I'm ready when you are.

4. Here’s the English translation of your question: At a certain fixed rate of simple interest, if a principal amount becomes double in \(x\) years and triple in \(y\) years, then what is the ratio \(x:y\)?

(a) 2:3 (b) 1:2 (c) 3:2 (d) 2:1

5. At an annual simple interest rate of 5%, a person deposits some money in the bank. After 5 years, how much total amount will he receive, if the principal is 12,500 rupees less than the total amount (principal + interest?

6. Under the same simple interest rate, a principal amount grows to 7000 rupees in 5 years and 8200 rupees in 8 years. What is the rate of interest?

(a) 4% (b) 6% (c) 8% (d) 10%

7. Some money becomes 5 times its original amount in 5 years at simple interest. At the same rate of interest, the time required for that principal to become 17 times is:

(a) 17 years (b) 20 years (c) 18 years (d) 19 years

8. If a principal amount doubles in \(x\) years, what is the annual rate of simple interest?

9. A farmer deposits ₹100 at the post office on the first day of every month. If the annual rate of simple interest is 5%, what will be the total amount (principal + interest) he receives at the end of the year?

10. If the ratio of the principal to the amount after annual compound interest is 25 : 27, then what is the rate of interest?

(a) 6% (b) 8% (c) 10% (d) 12%

11. 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)?

12. 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?

13. 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?

14. At an annual simple interest rate of \(\cfrac{a}{5}\)%, if the interest on ₹\(a^2\) for \(\cfrac{a}{3}\) years equals the principal amount, then what is the value of \(\cfrac{a^3}{60}\)?

15. If the compound principal of a certain principal amount after 4 years becomes \(\cfrac{256}{81}\) times the principal, then what is the interest rate?

(a) 15% (b) 30% (c) 33\(\cfrac{1}{3}\)% (d) 25%

16. If the ratio of the principal amount to its increased value after one year is 25:27, then what will be the annual interest rate?

(a) 2% (b) 4% (c) 6% (d) 8%

17. 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.

18. What would be the annual simple interest rate (percentage) if the interest for 4 years on a certain amount is \(\cfrac{8}{25}\) of the principal?

19. 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?

20. If a principal becomes \(3\frac{3}{8}\) times the original amount in 3 years at compound interest, what is the annual rate of interest?

21. At an annual simple interest rate of 6%, the interest for 5 months is \(\cfrac{x}{10}\) rupees. What will the principal be?

(a) ₹ 2x (b) ₹ 4x (c) ₹ 10x (d) ₹ 20x

22. If the total interest on a principal amount in 4 years is \(\cfrac{1}{5}\) of the principal, the annual rate of interest is:

(a) 4% (b) 5% (c) 10% (d) 20%

23. If the total amount becomes 966 rupees at an annual simple interest rate of 3% in 5 years, the principal amount will be -

(a) 480 rupees (b) 408 rupees (c) 404 rupees (d) 840 rupees

24. At an annual simple interest rate of \(r\%\), if the total interest on a principal for \(n\) years is \(\cfrac{pnr}{25}\) rupees, then the amount of the principal is –

(a) \(2p\) rupees (b) \(4p\) rupees (c) \(\cfrac{p}{2}\) rupees (d) \(\cfrac{p}{4}\) rupees

25. At an annual simple interest rate of \(x\%\), if the interest on a principal amount for \(x\) years is \(x\) rupees, what is the principal amount?

(a) \(x\) rupees (b) \(100x\) rupees (c) \(\cfrac{100}{x}\) rupees (d) \(\cfrac{100}{x^2}\) rupees

26. If the annual simple interest on a principal is \(\cfrac{1}{9}\) of it, then what will be the accumulated amount in 4 years if the total sum becomes 1326 rupees?

(a) ₹ 1080 (b) ₹ 1120 (c) ₹ 918 (d) ₹ 750

27. At what annual interest rate will the interest on a principal amount become \(\cfrac{5}{16}\) of the principal in 6\(\cfrac{1}{4}\) years?

(a) 3% (b) 4% (c) 5% (d) 6%

28. A person deposits two separate amounts in a bank at an interest rate of 10% per annum for 5 years. At the end of the term, they receive a difference of 2500 rupees in interest. What was the difference in principal amounts?

(a) ₹ 2000 (b) ₹ 5000 (c) ₹ 10000 (d) ₹ 4000

29. If the ratio of the principal to its total amount after one year is 25:28, then the annual interest rate is—?

(a) 3% (b) 12% (c) 10\(\frac{5}{7}\)% (d) 8%

30. What should be the annual rate of simple interest (in percentage) so that the interest earned in 4 years becomes \( \frac{2}{5} \) of the principal amount?