1. A certain sum of money amounts to ₹944 in 3 years at simple interest. If the rate of interest is increased by 25%, the same sum amounts to ₹980 in the same time period. Find the principal amount and the original rate of interest.

2. 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) ₹ \(\cfrac{200}{6}\)

3. Some money amounts to 944 rupees in 3 years at simple interest. If the annual rate of interest increases by 25%, then the same money amounts to 980 rupees in the same time. Find the rate of interest and the principal.

4. 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.

5. At the same rate of simple interest, a certain principal amounts to ₹1056 in 4 years and ₹1248 in 7 years. Find the rate of interest and the principal.

6. If a certain principal amount amounts to ₹1248 in 7 years and ₹1056 in 4 years at the same annual rate of simple interest, find the principal and the annual rate of simple interest.

7. When Mr. Subir retired from his job, he received a lump sum of ₹6,00,000 from his Provident Fund and Gratuity. He wants to divide this amount between the post office and the bank in such a way that he earns ₹34,000 annually as interest. If the annual simple interest rates of the post office and the bank are 6% and 5% respectively, determine how much money he should deposit in each.

8. 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%

9. Ramen Babu deposited a total of ₹370,000 across three banks. The annual simple interest rates for these three banks are 40%, 5%, and 6%, respectively. After one year, the amount of interest he earns from each bank is the same. Let us calculate how much money he deposited in each of the three banks.

10. 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.

11. 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

12. 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.

13. 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.

14. The simple interest on ₹400 for 5 years and on ₹600 for 4 years together amounts to ₹132. If the rate of interest is the same in both cases, find the rate of interest.

(a) 3% (b) 5% (c) 7% (d) 9%

15. Under the same rate of interest, the simple interest on ₹800 for 3 years and ₹1000 for 5 years together amounts to ₹592. What is the rate of interest?

(a) 6% (b) 8% (c) 7% (d) 9%

16. 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.

17. 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?

18. 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?

19. 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

20. 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

21. 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

22. 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

23. 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?

24. 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.

25. 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

26. ₹1200 is lent at an annual interest rate of 6\(\frac{1}{4}\)% and ₹1000 is lent at an annual interest rate of 4\(\frac{1}{3}\)% on the same day. After how much time will the amounts (principal + interest) of both loans become equal?

(a) 20 years (b) 24 years (c) 15 years (d) 30 years

27. If the simple interest on ₹850 for 3 years and on ₹1250 for 4 years at the same rate amounts to ₹302 in total, then what will be the annual rate of interest?

(a) 3% (b) 5% (c) 7% (d) None of the above

28. At an annual interest rate of 10%, compounded semi-annually, the difference between the compound interest and simple interest over 2 years is ₹124.05. Find the principal amount.

29. Bimalkaku deposited ₹187,500 in a bank at an annual 5% simple interest for his 12-year-old son and 14-year-old daughter, in such a way that when both of them turn 18, they will each receive the same amount of money (principal + interest). How much money did he deposit for his son and daughter respectively?

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