Students and Teachers Forum

1. The rates of increase of the population in first two years were 2% and 2.5%. Due to some epidemic diseases, it decreased by 1% in the third year. If the population of the district 3 years ago was 200000, what is the present population? By how much did the population increase in 3 years?

Given,        Rate of population growth in first year (R1) = 2%        Rate of population growth in second year (R2) = 2.5%        Rate of population decrement in third year (R3) = .....

2. The population of a certain village was 20000 some years ago. If the population of that village now is 21632 and the annual growth rate of the population is 4%, how many years ago it was 20000?

Given,           Population of a village some years ago (P) = 200000           Population of the village now (PT) = 21632           Growth rate of the population (R) = .....

3. A machine of Rs.10000 is depreciated at 10% per annum. Find its value after one year.

Here,     Original price (P) = Rs.10000     Rate (R) = 10%     Time (T) = 1 year We know,       Value of machine after one year = Rs. 10000 - 10% of Rs.10000             .....

4. The population of a town 2 years before was 252000. The population of the town increases in two successive years by 3% and 4% respectively, find the present population.

Given,        Time (T) = 2 years         Population before 2 years (P) = 252000         Rate of population growth in first year (R1) = 3%         Rate of population .....

5. The present cost of a bicycle is Rs. 3240. If the compound rate of depreciation is 5% p.a. what will it cost next year? What will be the amount of depreciation in 1 year?

Given,        Present cost of bicycle (P) = Rs. 3240        Rate of compound depreciation (R) = 5% p.a.        Time (T) = 1 year        Cost after one year (DT) = .....

6. A motor cycle purchased a year ago was depreciated at the rate of 15% p.a. If it is sold for Rs. 97750 now, what was its cost a year ago?

Given,         Rate of depreciation (R) = 15%         Selling price of the motorcycle (DT) = Rs. 97750         Time (T) = 1 year         Original price (P) = ? We .....

7. A man purchased a tempo for Rs. 240000. With the use of the tempo, he earned a profit of Rs. 48600 in 2 years. If he sold the tempo after 2 years at the rate of compound depreciation of 8% p.a. what does he gain or loss in 2 years?

Given,         Cost price of the tempo (P) = Rs. 240000         Profit earned = Rs. 48600         Time period (T) = 2 years         Rate of depreciation (R) = 8% We .....

8. In how many years will a video camera costing Rs. 48000 be reduced to Rs. 34680 if the rate of depreciation of the camera is 15% p.a.?

Given,          Cost price of the camera (P) = Rs. 48000          Depreciated price of the bus (DT) = Rs. 34680          Rate of depreciation (R) = 15%       .....

9. The population of a town is 185220. If the annual population growth is 5% p.a., what will be the population of the town after 3 years?

Given,         Initial population (P) =185220         Time (T) = 3 years         Growth rate (R) = 5%         Population after 3 years (PT) = ? We have,    .....

10. 2 years ago the population of a village was 1250. If the population growth rate is 2.5% p.a., find the present population.

Given,         Initial population of village (P) = 1250         Time period (T) = 2 years         Rate of growth (R) = 2.5%         Present population (PT) = ? We .....

11. Population of a village is 6400. It increases at the rate of 5% per annum. What will be the population after one year?

Given,         Initial population = 6400         Time = 1 year         Growth rate = 5%. Now,          Population after one year = 6400 +  5% of 6400   .....

12. The population of a village was 7200. 5% of the population migrated out and 2% died due to different causes within a year. What would be the population of the village after a year?

Given,      Original population (P) = 7200      Percentage of people migrated out = 5%      Percentage of people died = 2% So,         Depreciation rate(R) = 5% + 2%   .....

13. The population of a village was 10000 one year ago. The population at present is 9790, find the population decreasing rate.

Given, Population of the village one year ago = 10000 Population of the village at present = 9790 Population decreasing rate = ? Here, Decrease in population = 10000 - 9790                     .....

14. A bicycle of Rs. 3000 is depreciated in a year by 30%, find the amount of depreciation.

Here, Initial cost of bicycle (P) = Rs. 3000 Rate of depreciatin (R) = 30% Amount of Depreciation = ? We know, PT = P (1 + R100)T       = 3000 ( 1 - 30100)1       = .....

15. The difference between the compound interest and simple interest on a sum of money for 2 years at the rate of 10% p.a. is Rs. 240. Find the sum borrowed and the compound interest.

Let the sum be Rs. P. Then, Time (T) = 2 years Rate (R) = 10% p.a. Principal (P) = ? Compound Interest (CI) = ? According to the question, Compound interest (CI) – Simple interest (SI) = 240 We know, Compound interest (CI) = P [(1 + R100)T .....

16. A man deposited a sum of Rs.12500 in the bank at the compound rate of interest for 2 years. If the rate of interest for the first and the second year be 6% and 5% respectively,
(i) how much amount will he get in 2 years?
(ii) how much compound interest will he gain?

Given,       Principal (P) = Rs.12500       Time (T) = 2 years       Rate for first year (R1) = 6%       Rate for second year (R2) = 5%       Compound amount (CA) = ?   .....

17. Ram lends a sum of Rs.5000 to Krishna and Sundar for 2 years. Krishnan agrees to pay 12% p.a. simple interest and Sundar agrees to pay the same rate of compound interest. If at the end of 2 years, Krishna paid Rs.112.32 more than Sundar as the interest, find how much did he lend to each?

Given, Sum of money lent to Krishna and Sundar = Rs. 5000 Time period (T) = 2 years   Let the sum of money invested to Krishna and Sundar be Rs.x and Rs. (5000 – x) respectively. Then,  For Krishna, Principal (P) = Rs. x Rate (R) = .....

18. The difference between the compound interest and the simple interest on a sum of money at 12% p.a. for 2 years is Rs. 180. Find the sum, the simple interest and the compound interest.

Let the sum be Rs. P. Rate (R) = 12% Time (T) = 2 years Principal (P) = ? Simple interest (SI) =? Compound interest (CI) = ?  According to question,                   Compound interest (CI) – .....

19. Madan borrowed Rs.10,000 for 2 years at 10% p.a simple interest from Prakash and he immediately lent the sum to Bhuvan for the same time at the same rate of compound interest. How much did Madan gain in 2 years?

Given,       Principal (P) = Rs.10,000      Time (T) = 2 years       Rate (R) = 10% p.a. Then, Simple interest (SI) = PTR100                       .....

20. A sum of money invested at the compound interest payable yearly amounts to Rs. 6050 in 2 years and Rs. 6655 in 3 years. What are the amount of sum and the rate of interest?

Let the sum of money be Rs. x. According to question, When, Time (T1) = 2 years Amount (A1) = Rs. 6050 We know, Amount (A1) = P (1 + R100)T1        Or, 6050 = x (1 + R100)2 .....

21. The simple interest on a sum of money at the rate of 5% p.a. for two years is Rs. 200. Find the compound interest on the same sum at the same rate for the same time.

Given,      Simple interest (SI) = Rs. 200      Rate (R) = 5% p.a.      Time (T) = 2 years We know,            SI = PTR100            Or, 200 .....

22. A invested Rs.25000 for 3 years at the rate of 12% simple interest per annum and B invested the same amount for the same time at the rate of 10% per annum compound interest. Calculate the interest received by A and the interest received by B.

Given, For A,        Principal (P) = Rs.25000        Time (T) = 3 years        Rate (R) = 12% We know, Simple interest (SI) = PTR100                 .....

23. At what rate of compound interest will a sum of Rs. 640 amount to Rs.1250 in 3 years?

Given,          Principal (P) = Rs. 640          Compound amount (CA) = Rs. 1250          Time (T) = 3 years          Rate of interest (R) = ? We .....

24. Find the difference between the simple interest and the compound interest on Rs. 7500 in 2 years at 10% per annum.

Given,          Principal (P) = Rs.7500          Time (T) = 2 years          Rate of interest (R) = 10%          Difference between SI and CI = .....

25. In how many years will a sum of Rs. 2500 amount to Rs. 3600 at 20% p.a. the interest being compounded annually?

Given,        Principal (P) = Rs. 2500        Compound amount (CA) = Rs. 3600        Rate of interest (R) = 20%        Time period (T) = ? We know,       .....

26. A man borrowed Rs. 50000 for 3 years at compound interest. If the rate of interest is 3% p.a for the first year, 4% p.a. for the second year and 5% p.a for the third year, how much should he repay at the end of 3 years?

Given,      Principal (P) = Rs. 50000      Time (T) = 3 years      Rate for 1st year (R1) = 3%      Rate for 2nd year (R2) = 4%      Rate for 3rd year (R3) = 5% We .....

27. Find the rate of compound interest when Rs. 5120 amounts to Rs. 7290 in 1½ years if the interest is compounded half yearly.

Given, Principal (P) = Rs. 5120 Compound amount (CA) = Rs.7290 Time (T) = 1 ½ years                = 1.5 years We know, For interest compounded half yearly, Compound amount (CA) = P (1 + R200)2T   .....

28. At what rate of compound interest would Rs.8000 amount to Rs.8820 in two years, interest being compounded yearly?

Given, Principal (P) = Rs. 8000 Compound Amount (CA) = Rs.8820 Time (T) = 2 years Rate of interest (R) = ? We know, Compound amount (CA) = P (1 + R100)T         Or,                  .....

29. The compound interest on a sum of money in 2 years at the rate of 10% p.a. is Rs. 20.50 more than the simple interest. Find the sum.

Here,        Let the sum be Rs. P.        Rate (R) = 10%        Time (T) = 2 years According to question,             Compound interest (CI) – Simple .....

30. Find the compound interest on Rs. 6400 for 2 years if the rate of interest for the first year is 5% p.a. and for the second year is 10% per annum.

Given,       Principal (P) = Rs. 6400       Time (T) = 2 years       Rate for 1st year (R1) = 5%      Rate for 2nd year (R2) = 10% We know, Compound Amount (CA) = P (1 + R1100) (1 + .....

31. The simple interest on a sum of money in 2 years is Rs.128 less than the compound interest. If the rate of interest is 8% p.a., find the sum.

Let the sum be Rs. P. Rate (R) = 8% Time (T) = 2 years According to question,               Compound interest (CI) – Simple interest (SI) = Rs.128        Or , P [(1 + R100)T - 1] - .....

32. The compound interest on a sum P in T years at r% per annum is CI. Write down the relation between P, T, r and CI.

Here, Time = T, Rate = r  Sum = P The relation between P, T, r and CI is given by,   CI= P[(1 + R100)T -1], which is the required .....

33. Find the simple interest on the sum Rs. 2000 for 3 years at 10% rate of interest.

Given, Sum (P) = Rs.2000 Time (T) = 3 yrs Rate (R) = 10% Simple interest (SI) = ? We know, Simple interest =  PTR100                           = Rs. 2000 ⨉ 3 ⨉ .....

34. A finance company’s share price depreciated at the rate of 8% p.a for 3 years. If Rs. 48668 is the value of the shares at present, how many shares each of Rs. 100 were sold 3 years ago?

Given,        Rate of depreciation (R) = 8%        Time (T) = 3 years        Value of share at present (DT) = Rs. 48668 We know,       DT = P (1 - R100)T Or, 48668 = P (1 - .....

35. Find the compound amount and the compound interest on Rs. 12000 at 8% p.a. in 2 years, the interest being added half yearly.

Given,         Principal (P) = Rs. 12000         Rate of interest (R) = 8% p.a         Time (T) = 2 years         Compound amount (CA) = ?         .....

36. Prove that the simple interest and the compound interest for unit period of time are equal for same principal and rate of interest?

Here,   For time period (T) =1 year, simple interest (SI) is given by,   SI = PR100 And,         Compound interest (CI)  = P [(1+R100) -1]             .....

37. The compound interest of a sum of money in  1 year and 2 years are Rs. 450 and and Rs. 945 respectively. Find the rate of interest compounded yearly and the sum.

Given, Compound interest (CI) = Rs. 450 when time (T) = 1 year  Compound interest (CI) = Rs. 945 when time (T) = 2 years Let the sum be x and the rate be r. Then , CI = P[ (1 + R100)T - 1 ] From the 1st case, 450 = x [(1+r100 ) - 1 .....

38. Prativa deposited Rs. 150000 in a bank at the rate of 10% p.a. Pramila deposited Rs. 150000 in the bank at the rate of 12% p.a. If Prativa received semi-annual compound interest and Pramila received annual compound interest, which interest is more and by how much in 3 years? Find it.

 

Here,        Principal amount (P) = Rs. 150000        Time period (T) = 3 years Now,           Compound interest received semi-annually by Prativa at 10% is given by,     .....

39. According to yearly compound interest, a sum of money amounts to Rs. 6050 in 2 years and Rs. 6655 in 3 years. What was the sum?

Given, Compound amount (CA) = Rs. 6050 when Time (T) = 2 years Compound amount (CA) = Rs. 6655 when Time (T) = 3 years Sum of money (P) = ? Let the sum be ‘x’ and the interest be ‘r’ So, from the 1st case,     .....

40. What is the compound amount on Rs. 2500 at the rate of 8% for 2 years?

Here, Principal amount (P) = Rs. 2500, Rate of interest (R) = 8% and Time (T) = 2 years Compound Amount (CA) = ? CA = P(1+R100)T        = 2500(1+8100)2         = 2500(1.08)2        .....

41. Rs. 80000 is deposited in a bank, which of the following option is the best for withdrawing the entire amount after 2 years?
i.  12% annually compound interest rate. 
ii. 10% semi-annually compound interest rate.
 

Here,        Principal amount (P) = Rs. 80000        Time period (T) = 2 years i. 12% annually compound interest is given by,     CI1 = P1+R100T-1            =Rs. 80000 .....

42. In what time will a sum of Rs. 1500 yields Rs.196.50 as compound interest at 12% per annum compounded semi-annually?

Given,        Principal (P) = Rs.1500        Compound interest (CI) = Rs. 196.50        Rate (R) = 20%        Time period (T) = ? We know,      For .....

43. Neema borrowed Rs. 24000 from a commercial bank for 3 years at the rate of 12.5% p.a. in simple interest. She lent the money to Sangita in compound interest at the same rate. How much will she have profit after 3 years? Find it.

Here,        Principal amount (P) = Rs. 24000        Rate of interest(R) = 12.5%        Time period (T) = 3 years Now, Simple interest = PTR100             .....

44. The compound interest on a sum of money in 2 years at 5% p.a. will be Rs.120 more than the simple interest. Find the sum and the compound interest.

Let the sum be Rs. P. Then, Time (T) = 2 years Rate (R) = 5% p.a. Principal (P) = ? Compound interest (CI) = ? According to the question, Compound interest (CA) – Simple interest (SI) = 120 We know, Compound interest (CI) = P [(1 + R100)T .....

45. Roshan borrowed a sum of money in simple interest at 5% p.a. for 4 years and he immediately lent the sum to Ramkali in compound interest at the same rate. He made a profit of Rs. 30 after 4 years. How much sum was borrowed by Roshan?

Here,      Principal amount = P (say)      Interest rate (R) = 5%     Time period(T) = 4 years     Amount of sum borrowed (P) = ? From question,           Profit = Rs. .....

46. Mohan lends altogether Rs. 6600 to Ram and Shyam for 2 years. Ram agrees to pay simple interest at 15% p.a. and Shyam agrees to pay compound interest at the same rate. If Ram paid Rs. 261 more than Shyam as the interest, find how much did he lend to each.

Here, Let the amount lent to Ram is Rs.x. Then, Time (T) = 2 years Rate of interest (R) = 15% We know, Simple interest (SI) = PTR100                                 = x .....

47. If A is the compound amount, r is the rate percent per annum and T is the time period, what will be the principal?

Here, Amount = A Rate percent per annum = r Time period = T Then, the principal is given by, P = A / (1+ r / .....

48. What sum invested at the rate of 5% p.a. for 2 years will earn Rs. 82.41 as the compound interest, the interest being payable yearly?

Given,         Rate of interest (R) = 5% p. a.         Time (T) = 2 years         Compound Amount (CI) = Rs.82.41.         Sum invested (P) = ? We know,     .....

49. At what rate of compound interest would Rs. 8000 amount to Rs. 8820 in two years, interest being compounded yearly?

Given,          Principal (P) = Rs. 8000         Compound Amount (CA) = Rs. 8820         Time (T) = 2 years         Rate of interest (R) = ? We know,     .....

50. According to the system of yearly compound interest, a sum of money invested in 2 years amounts to Rs.7260 and in 3 years it amounts to Rs.7986. Find the sum invested and the rate of compound interest.

Let the sum of money be Rs. x. According to question, When,     Time (T1) = 2 years Amount (A1) = Rs. 7260 We know, Amount (A1) = P (1 + R100)T1 Or, 7260 = x (1 + R100)2 .....