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 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%

3. If the ratio of the principal and the annual compound amount is 10:11, then the annual interest rate is _____.

4. If the ratio of principal to interest-principal in a year is 8:9, then what is the annual simple interest rate?

(a) 12\(\cfrac{1}{2}\)% (b) 15\(\cfrac{1}{2}\)% (c) 12% (d) 15%

5. 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

6. 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%

7. A certain amount of money amounts to ₹700 in 4 years at simple annual interest, and during this time the interest is 40% of the principal. What is the amount of the principal?

(a) ₹ 500 (b) ₹ 400 (c) ₹ 600 (d) ₹ 300

8. A person deposited ₹100 in a bank, and after 2 years received ₹121 as the total amount under compound interest. What is the annual percentage rate of compound interest?

9. If the ratio of a principal amount and its amount after 5 years is 5 : 6, then find the annual simple interest rate.

10. If the ratio of principal to amount after 1 year is 20 : 21, what is the annual rate of simple interest (in percentage)?

11. 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?

12. If after one year the ratio of the principal to the amount (principal + interest) is 10 : 12, what is the annual rate of simple interest (in percentage)?

13. 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%

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 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?

16. 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?

17. If a certain principal amounts to ₹1500 at an annual interest rate of 10% and ₹1300 at an annual interest rate of 6% after a fixed period, what is the principal?

(a) ₹ 500 (b) ₹ 1000 (c) ₹ 1800 (d) ₹ 1600

18. At a fixed time, a certain amount of money amounts to ₹400 at an annual interest rate of 10% and ₹200 at an annual interest rate of 4%. What is the principal?

(a) ₹ \(\cfrac{100}{6}\) (b) ₹ \(\cfrac{100}{3}\) (c) ₹ \(\cfrac{200}{3}\) (d) ₹ \(\cfrac{200}{6}\)

19. If a certain principal amount accrues to ₹950 at an annual interest rate of 10% and ₹700 at an annual interest rate of 6% over the same period, then the duration of time is –

(a) 13\(\cfrac{3}{19}\) years (b) 3\(\cfrac{3}{19}\) years (c) 19\(\cfrac{3}{13}\) years (d) none of the above

20. If the ratio of a certain principal amount to its compound amount after a certain period is 15:21 and the annual simple interest rate is 5%, then the duration of time is –

(a) 4 years (b) 2 years (c) 8 years (d) 10 years

21. If the ratio of a certain principal amount to the interest accrued over a given period is 20:7, and the annual simple interest rate is 6%, then the duration of time is –

(a) 6 years (b) 5\(\cfrac{5}{6}\) years (c) 6\(\cfrac{5}{7}\) years (d) none of the above

22. 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%

23. If the ratio of the principal to the total amount (principal + interest) in one year is \(4:9\), determine the annual simple interest rate.

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 the ratio of the principal amount and the amount with interest after 1 year is 8:9, then the annual simple interest rate is 12.5%.

26. 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?

27. If ₹800 is deposited in a bank at an annual simple interest rate of 10%, and the total amount received (principal + interest) is ₹1200, then calculate and write for how long the money was deposited in the bank.

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. A person deposited ₹100 in a bank, and after 2 years received a total of ₹121 with compound interest. What is the annual compound interest rate?

(a) 10% (b) 20% (c) 5% (d) \(10\cfrac{1}{2}\)%

30. Under the condition that no interest will be charged if the money is repaid within two years, three friends borrowed ₹6000, ₹8000, and ₹5000 respectively from a cooperative bank to jointly purchase four cycle rickshaws. After two years, after deducting all expenses, their total income amounted to ₹30,400. They divided this income in proportion to their capital contributions and then repaid their individual bank loans. Now, calculate how much money each person will have left in hand and what the ratio of the remaining amounts will be.