1. In how many years, at the rate of 8% per annum, will the ratio of the principal to the simple interest become 25 : 8?

(a) \(3\cfrac{1}{2}\) (b) 4 (c) 5 (d) \(5\cfrac{1}{2}\)

2. 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) \(\frac{1}{2}\)

3. 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.

4. Write down the calculation to determine in how many years a simple interest of ₹168 will be earned on a principal of ₹600 at an annual rate of 8%.

5. Rahmat Chacha borrowed ₹240000 from a bank at an annual simple interest rate of 12% to build a house. One year after borrowing, he started renting out the house for ₹5200 per month. Calculate and determine after how many years from borrowing he will be able to repay the bank loan along with interest using the rental income.

6. At an annual simple interest rate of 5%, how many years will it take for the interest on ₹6000 to become ₹1500?

(a) 3 years (b) 30 years (c) 5 years (d) 15 years

7. At an annual simple interest rate of 6%, in how many years will the interest on ₹\(x\) amount become ₹\(\frac{9x}{25}\)? Find the value of the time.

(a) 6 years (b) 8 years (c) 10 years (d) 12 years

8. What should be the annual rate of simple interest (in percentage) so that the interest earned in 4 years becomes \( \frac{2}{5} \) of the principal amount?

9. What should be the annual rate of simple interest (in percentage) so that the interest earned in 4 years becomes \(\frac{8}{25}\) of the principal amount?

10. 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.

11. 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?

12. A man takes a loan of ₹4,000 at 7% simple interest per annum, and exactly one year after the first loan, he takes a second loan of ₹4,000 at 4% simple interest per annum. After how many years from the first loan will the interest on both loans be equal?

13. 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.

14. 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.

15. Mr. Amal bequeaths ₹56,000 in his will for his two sons aged 13 and 15 in such a way that, when they each turn 18, the simple interest earned at an annual rate of 10% will be equal to the principal for each. What will be the allocated amount for each son in the will?

16. 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?

17. At an annual interest rate of 20%, for how much principal will the difference between compound interest and simple interest for 3 years be ₹1024?

(a) ₹ 2800 (b) ₹ 1100 (c) ₹ 8000 (d) ₹ 3000

18. Anil Babu wants to allocate ₹56,000 between his two sons, aged 13 and 15, such that when they turn 18, the simple interest earned at an annual rate of 10% is equal to their respective principal amounts. Determine the amount allocated to each son in the will.

19. Rokeya takes a loan from the bank under the condition that she will pay interest at an annual simple interest rate of 10% and repay \(\frac{1}{5}\) of the principal every two years. If she pays 10,000 currency units as the first installment after two years, determine the amount she borrowed.

20. A person borrows ₹2,40,000 at an annual simple interest rate of 12% to build a house. One year after taking the loan, they start renting out the house for ₹5,200 per month. After how many years from taking the loan will the rental income be enough to repay the entire loan along with the accrued interest?

21. Mr. Rathin deposits money in the bank for each of his two daughters in such a way that when each daughter turns 18 years old, she will receive ₹120000. The bank offers simple interest at an annual rate of 10%. The current ages of the daughters are 13 years and 8 years respectively. Calculate how much Mr. Rathin deposited in the bank for each daughter.

22. My aunt wants to will ₹56,000 between her two sons, aged 13 and 15, in such a way that by the time each turns 18, the total amount (principal + interest) received by both sons is equal. The interest is calculated at an annual simple interest rate of 10%. Determine how much should be allotted to each son in the will.

23. If the rate of simple interest and compound interest is 10% per annum, find the ratio of simple interest to compound interest for the second year on any principal.

(a) 20:21 (b) 10:11 (c) 5:6 (d) 1:1

24. 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

25. At an annual simple interest rate of 5%, a person deposits some money in the bank. After 5 years, how much total amount will he receive, if the principal is 12,500 rupees less than the total amount (principal + interest?

26. A principal amount doubles in 20 years at a certain simple interest rate. At the same rate of simple interest, the time required for the principal to become three times will be:

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

27. 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

28. If the time period and the annual simple interest rate are equal, then at what annual interest rate will the interest amount be \(\cfrac{1}{25}\) of the principal?

(a) 25% (b) 10% (c) 2% (d) 2.5%

29. If the annual interest rate and time period are equal, in how many years will the interest on 144 rupees become 25 rupees?

(a) 4 years (b) \(4\cfrac{1}{6}\) years (c) 6 years (d) \(6\cfrac{1}{4}\) years

30. ₹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