1. A certain principal doubles in 20 years at a fixed simple interest rate. At the same rate of simple interest, the principal will become four times in—?

(a) 40 years (b) 60 years (c) 80 years (d) none of the above

2. A principal amount doubles in 20 years at a certain simple interest rate. At the same rate, in how many years will the principal become three times?

3. 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

4. If a principal doubles in 20 years with simple interest, then at the same simple interest rate, the principal will become four times in –

(a) 30 years (b) 40 years (c) 80 years (d) 60 years

5. A certain principal doubles in 20 years at a given rate of simple interest. At the same rate of simple interest, that principal will become triple in —

(a) 30 years (b) 35 years (c) 40 years (d) 45 years

6. If a certain principal amount becomes 5 times its original value in 20 years due to interest, then the rate of interest is –

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

7. 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.

8. 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.

9. 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

10. If a principal amount yields a total of ₹7,100 (principal + simple interest) in 7 years and ₹6,200 in 4 years at the same annual rate of simple interest, find the principal and the annual rate of simple interest.

11. 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.

12. If a principal amount doubles in 20 years at a certain simple interest rate, then in how many years will it triple at the same simple interest rate?

13. If a principal amount doubles in 20 years at a certain simple interest rate, then at the same rate, the principal will triple in – ?

(a) 30 years (b) 35 years (c) 45 years (d) 40 years

14. 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

15. At an annual simple interest rate of 8%, how much interest will make the principal amount grow to \(\cfrac{7}{5}\) times its original value?

(a) 4 years (b) 5 years (c) 6 years (d) 7 years

16. 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%

17. 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

18. If a certain principal amount triples in 15 years at simple interest, then the annual rate of simple interest will be —

(a) \(13\frac{1}{3}\%\) (b) \(12\frac{1}{3}\%\) (c) \(11\frac{1}{3}\%\) (d) \(10\frac{1}{3}\%\)

19. If a principal amount doubles in 8 years at an annual compound interest rate of \(r\%\), then in how many years will it become four times?

20. 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)?

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

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. 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

24. At an annual interest rate of \(6\cfrac{2}{3}\%\), determine the time required for the amount to become \(1.5\) times the principal.

25. At an annual simple interest rate of 10%, determine the time required for a principal amount to double.

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

26. In how many years will the amounts of simple interest and compound interest be equal for the same principal at the same annual interest rate?

(a) 3 years (b) 2 years (c) 1 years (d) \(\frac{1}{2}\)

27. 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.

28. At the same interest rate, the simple interest on a certain amount for 3 years is ₹1200, and the compound interest for 2 years is ₹832. Determine the interest rate and the principal amount.

29. What should be the annual interest rate (percentage) for a principal amount to become three times its original value in 25 years?

30. At an equal annual interest rate, determine the number of years required for the simple interest and compound interest on a given principal to become equal.