1. 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

2. At an annual simple interest rate of \(x\%\), the interest on 120 rupees for 10 months will be _____ rupees.

3. 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.

4. 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

5. The simple interest on ₹\(b\) for \(c\) months at an annual rate of \(a\%\).

(a) \(\cfrac{abc}{1200}\) (b) \(\cfrac{abc}{100}\) (c) \(\cfrac{abc}{200}\) (d) \(\cfrac{abc}{120}\)

6. 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?

7. 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

8. At an annual simple interest rate of \(X\%\), the interest on \(Y\) taka for \(Z\) months will be.

(a) \(\cfrac{XYZ}{1200}\) rupees (b) \(\cfrac{XYZ}{100}\) rupees (c) \(\cfrac{XYZ}{200}\) rupees (d) 0\(\cfrac{XYZ}{120}\)rupees

9. 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

10. 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

11. What should be the annual rate of simple interest so that the interest for 5 years becomes \(\frac{1}{4}\) of the principal?

12. At an annual interest rate of 10%, the compound interest on ₹\(x\) for 2 years is ____ rupees.

13. 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)?

14. Doubling the principal means Principal \((p) =\) Interest \((I) = x\) taka Rate of interest \((r) = 6\frac{1}{4}\% = \frac{25}{4}\%\) \[ \therefore \text{Time } (t) = \frac{100 \times I}{p \times r} \text{ years} = \frac{100 \times x}{x \times \frac{25}{4}} = \frac{100 \times 4}{25} = 16 \text{ years} \] \[ \therefore \text{At an annual simple interest rate of } 6\frac{1}{4}\%, \text{ any principal will double in 16 years.} \]

15. Sure! The Bengali sentence: **"কোনো মূলধন বার্ষিক 6 \(\frac{1}{4}\)% সরল সুদের হারে কত বছরে দ্বিগুণ হবে তা লিখি ।"** translates to English as: **"Write how many years it will take for a principal to double at an annual simple interest rate of 6 \(\frac{1}{4}\)%."** Would you like help solving this too?

16. What should be the annual simple interest rate (in percentage) so that the interest on a sum of money for 6 years becomes \(\frac{18}{25}\) of the principal?

17. If the interest is compounded every 6 months at an annual rate of 10%, then calculate the compound interest and the total amount on ₹1600 for \(1\cfrac{1}{2}\) years.

18. If the simple interest on \(a\) INR for \(b\) months is \(c\) INR, then the annual percentage interest rate will be? (Question)

(a) \(\cfrac{1200a}{bc}\%\) (b) \(\cfrac{1200c}{ab}\%\) (c) \(\cfrac{100b}{ac}\%\) (d) \(\cfrac{100ac}{ab}\%\)

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

20. Simple interest for 800 rupees at an annual rate of \(6\frac{1}{4}\%\) for 6 years.

(a) ₹ 300 (b) ₹ 240 (c) ₹ 250 (d) none of the above

21. 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?

22. What should be the annual simple interest rate so that the interest for 5 years becomes \(\cfrac{1}{4}\) of the principal?

23. Determine the annual simple interest rate (in percentage) at which the interest for 5 years becomes \(\cfrac{2}{5}\) of the principal amount.

24. Calculate the amount on ₹960 at an annual simple interest rate of \(8\frac{1}{3}\%\) for 1 year and 3 months.

25. Write how many years it will take for a principal to double at an annual simple interest rate of 6 \(\frac{1}{4}\)%.

26. At an annual simple interest rate of \(r\%\), the interest on 100 rupees for 1 year is \(\cfrac{r}{100}\) times the principal.

27. At an annual simple interest rate of \( \cfrac{a}{5} \)% on \( a^2 \) rupees for \( \cfrac{a}{3} \) years, if the interest is \( \cfrac{a^3}{60} \), find the value of \( a \).

28. 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%

29. At an annual simple interest rate of \(3\frac{1}{2}\%\), what is the simple interest on ₹750 for 73 days?

(a) ₹ 5.25 (b) ₹ 5.75 (c) ₹ 6 (d) None of the above

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