1. If an amount becomes 520 rupees in 5 years and 568 rupees in 7 years, then the principal amount is—

(a) ₹ 400 (b) ₹ 500 (c) ₹ 600 (d) ₹ 700

2. 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?

3. 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

4. A principal amount increases by \(\cfrac{1}{8}\) of itself every year. If it becomes 900 rupees in 7 years, then what was the initial principal amount?

(a) ₹ 400 (b) ₹ 600 (c) ₹ 800 (d) ₹ 480

5. 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?

6. 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

7. If the interest on a principal amount becomes \(\cfrac{3}{8}\) of the principal in 5 years, what is the rate of interest?

(a) 6% (b) 7.5% (c) 8% (d) 10.5%

8. 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%

9. 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.

10. If a certain principal amount becomes ₹1,00,000 in 3 years and ₹1,72,800 in 6 years at compound interest, then what is the interest rate?

(a) 10% (b) 20% (c) 25% (d) 15%

11. 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.

12. 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

13. 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.

14. At an annual simple interest rate of 10%, if the interest for 5 years is x rupees, then the principal amount:

(a) ₹ 2x (b) ₹ 4x (c) ₹ 10x (d) ₹ 20x

15. 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

16. 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

17. The simple interest on a principal amount is \(\cfrac{1}{6}\) of it per year. If the total amount after 5 years is 2200 rupees, then the principal amount is—

(a) ₹ 1000 (b) ₹ 1200 (c) ₹ 1400 (d) ₹ 1600

18. If the simple interest for \(n\) years at an annual rate of \(r\%\) is \(\frac{pnr}{25}\) rupees, then the principal amount will be _____ rupees.

19. If the total simple interest on a principal amount at an annual rate of \(x\%\) for \(y\) years is \(\frac{pyx}{25}\) rupees, then the principal amount will be:

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

20. If a certain principal earns ₹560 in 3 years and ₹600 in 5 years at the same annual simple interest rate, find the amount of the principal and the annual rate of simple interest.

21. 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?

22. 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 \(\cfrac{a^3}{60}\)?

23. 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

24. 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%

25. If the difference between the compound interest and simple interest on a certain sum at a rate of 20% per annum for 3 years is ₹800, what is the principal amount?

(a) ₹ 5250 (b) ₹ 8650 (c) ₹ 6250 (d) none of the above

26. 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.

27. At an annual simple interest rate of \(x\%\), if the total interest on a principal amount for \(y\) years is \(\cfrac{xyz}{25}\) rupees, then the principal amount is –

(a) ₹ 2z (b) ₹ 4z (c) \(\cfrac{z}{2}\) (d) \(\cfrac{z}{4}\)

28. 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.

29. If a certain principal earns ₹560 in 3 years and ₹600 in 5 years at the same annual simple interest rate, determine the principal amount and the annual percentage rate of simple interest.

30. 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?