1. 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

2. 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) \(\cfrac{z}{4}\)

3. 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

4. At an annual simple interest rate of \(x\%\), if the interest earned in \(x\) years is ₹\(x\), then the amount of principal is —

5. 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

6. 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?

7. Translate: If the simple interest on a certain principal for \(n\) years at a rate of \(r\%\) is \(\frac{pnr}{25}\) rupees, then the amount of the principal is –

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

8. 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

9. 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

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

11. 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.

12. 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.

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 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

16. 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

17. At an annual simple interest rate of x%, if the interest earned in x years is x rupees, then the principal amount is —

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

18. At an annual interest rate of 9%, if the difference between the compound interest and simple interest on a certain amount for 2 years is ₹129.60, then calculate and write that principal amount.

19. 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.

20. If the simple interest on a certain principal for 1 year is ₹50 and the compound interest for 2 years is ₹102, then calculate and write the amount of the principal and the annual rate of interest.

21. At an annual interest rate of \( a\% \), if the interest for \( a \) years on a principal is \( b \) rupees, then the amount of the principal is—

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

22. If the interest on a principal for 5 years is \(\cfrac{1}{4}\) of the principal, then the annual interest rate will be –

(a) 5% (b) 10% (c) 15% (d) 20%

23. 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

24. At an annual simple interest rate of 12%, if the ratio of principal to interest after \(x\) years is 25:24, what is the value of \(x\)?

(a) 8 (b) 10 (c) 12 (d) 5

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

26. If the amount becomes ₹\(y\) in \(x\) years at an annual interest rate of 4%, then the principal (original amount) will be –

(a) ₹ \(4xy\) (b) ₹\(\cfrac{4x}{100+y}\) (c) ₹ \(\cfrac{100y}{100+4x}\) (d) ₹\(\cfrac{100x}{4}\)

27. Mr. Jayanta deposits ₹1,000 on the first day of every month in a monthly scheme. If the annual simple interest rate is 5%, then how much total amount (principal + interest) will he receive at the end of the year?

28. 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

29. If the interest accrued on a certain principal amount at an annual rate of 8% over 6 years is ₹144, then what is the principal amount?

(a) ₹ 1440 (b) ₹ 450 (c) ₹ 444 (d) ₹ 300

30. At an annual interest rate of 4%, the difference between the simple interest and compound interest on a principal amount for 2 years is 40 rupees. Determine the principal amount.