Profit and Loss

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Basic Exercise 3
BASIC EXERCISE 3
LOTS: Lower Order Thinking Skills
  1. The population of a village was 7,000 one year ago. If the population growth rate of the village is 3.1%, find the population at present.
  2. The population of a village was 5,400 one year ago. If the population growth rate of the village is 2.5%, find the population at present.
  3. The population of a village was 10,000 one year ago. The population at present is 10,210; find the population growth rate.
  4. The population of a village was 10,000 one year ago. The population at present is 9,780; find the population decreasing rate.
  5. The population of a village is 12,000. If the population is increased by 1,000 due to birth and 2,000 due to immigration, what will be the population of the town?
  6. The population of a village was 7,200. If 500 of the population migrated in and 200 died due to earthquake within a year, what will be the population of the village after a year?
  7. A telephone set costing Rs. 1,000 is depreciated at the rate of 10% p.a. Find the amount of price depreciation in 1 year.
  8. The population of a village was 7,000 one year ago. If the population growth rate of the village is 3.1%, find the population at present.
  9. The population of a village was 5,400 one year ago. If the population growth rate of the village is 2.5%, find the population at present.
  10. The population of a village was 10,000 one year ago. The population at present is 10,210; find the population growth rate.
  11. The population of a village was 10,000 one year ago. The population at present is 9,780; find the population decreasing rate.
  12. The population of a village is 12,000. If the population is increased by 1,000 due to birth and 2,000 due to immigration, what will be the population of the town?
  13. The population of a village was 7,200. If 500 of the population migrated in and 200 died due to earthquake within a year, what will be the population of the village after a year?
  14. A telephone set costing Rs. 1,000 is depreciated at the rate of 10% p.a. Find the amount of price depreciation in 1 year.
  15. After the continued revaluation of Pound Sterling for 2 years at 5% per year, Pound Sterling (£) 1 is equal to NC. Rs 154.35 at present. What was the Pound Sterling (£) 1 equal to NC. Rs before 2 years? Find it.
  16. The population of a village was 20,000. Within 2 years, the population is increased 3% by birth and 2% by immigration. What will be the population of the village after 2 years? Find it.
  17. The population of a place was 2000. Within a year the population is increased 3% by birth rate and 2% by migration. How much population is there now?
  18. The population of the Kathmandu valley in 2073 was 25 lakh approximately. If the population growth rate is 4% per annum approximately, what will be the increased population till the end of 2076? Find it.
  19. The growth rate of a plant is 2% per month. In the beginning of Poush 2072, if its height was 4 m, what height was increased in the beginning of Chaitra 2072?
  20. The population of a village was 10000 one year ago. The population at present is 10210. Find the population growth rate.
  21. The population of a village was increased from 10,000 to 11,000 in one year. Find out the population increasing rate.
  22. According to the population census B.S. 2068, the population of Pokhara at the end of B.S. 2068 was 2 lakh 80 thousands approximately. If the population at the end of B.S. 2071 was 3 lakh 24 thousand 135, find the population growth rate.
  23. In the beginning of 2069 B.S. and at the end of 2070 B.S., the population of a village was 5000 and 5408 respectively. What is the annual population growth rate? Find it.
  24. The present population of a town is 40000. If the population increases by 10% every year, after how many years the population of the town will be 53240? Find it.
  25. The present population of a town is 50000. If the population increases by 8% every year, after how many years the population of the town will be 58320? Find it.
  26. The value of a computer which was bought for Rs 40,000 depreciates at 10% annually. What will be the cost of the computer after 2 years?
  27. A farmer bought a tractor for Rs 400000 and sold it after 2 years at 10% depreciation rate per year. What is the cost of tractor after 2 years? Find it.
  28. After the continued revaluation of Pound Sterling for 2 years at 5% per year, Pound Sterling (£) 1 is equal to NC. Rs 154.35 at present. What was the Pound Sterling (£) 1 equal to NC. Rs before 2 years? Find it.
  29. The population of a village was 20,000. Within 2 years, the population is increased 3% by birth and 2% by immigration. What will be the population of the village after 2 years? Find it.
  30. The population of a place was 2000. Within a year the population is increased 3% by birth rate and 2% by migration. How much population is there now?
  31. The population of the Kathmandu valley in 2073 was 25 lakh approximately. If the population growth rate is 4% per annum approximately, what will be the increased population till the end of 2076? Find it.
  32. The growth rate of a plant is 2% per month. In the beginning of Poush 2072, if its height was 4 m, what height was increased in the beginning of Chaitra 2072?
  33. The population of a village was 10000 one year ago. The population at present is 10210. Find the population growth rate.
  34. The population of a village was increased from 10,000 to 11,000 in one year. Find out the population increasing rate.
  35. According to the population census B.S. 2068, the population of Pokhara at the end of B.S. 2068 was 2 lakh 80 thousand approximately. If the population at the end of B.S. 2071 was 3 lakh 24 thousand 135, find the population growth rate.
  36. In the beginning of 2069 B.S. and at the end of 2070 B.S., the population of a village was 5000 and 5408 respectively. What is the annual population growth rate? Find it.
  37. The present population of a town is 40000. If the population increases by 10% every year, after how many years will the population of the town be 53240? Find it.
  38. The present population of a town is 50000. If the population increases by 8% every year, after how many years will the population of the town be 58320? Find it.
  39. The value of a computer which was bought for Rs 40,000 depreciates at 10% annually. What will be the cost of the computer after 2 years?
  40. A farmer bought a tractor for Rs 400000 and sold it after 2 years at 10% depreciation rate per year. What is the cost of the tractor after 2 years? Find it.
  41. A factory was bought for Rs 400000 some years ago and now its value is Rs.196000. If the value of the factory is depreciated at 30% p.a., When was the factory bought?
  42. A factory was bought for Rs 300000 some years ago and now its value is Rs 243000. If the value of the factory is depreciated at 10% p.a., when was the factory bought?
SEE EXERCISE 3
  1. The present population of a rural municipality is 10,000 and the population is being increased by 2% every year.
    1. Write the formula to find population after T years if the initial population is P and the rate of annual growth is R%.
    2. What will be the population of the rural municipality after 3 years? Calculate it.
    3. In how many years will the population of the rural municipality be 10,404 at the same rate of population growth? Find it.
  2. The present population of a rural municipality is 40,000 and the population is being increased by 1% every year.
    1. Write the formula to find population after T years if the initial population is x and the rate of annual growth is r%.
    2. What will be the population of the rural municipality after 3 years? Calculate it.
    3. In how many years will the population of the rural municipality be 40,804 at the same rate of population growth? Find it.
  3. The present population of a municipality is 20,000 and the annual population growth rate is 3%.
    1. Write the formula to find the population after T years if the initial population is P and the rate of annual growth is R.
    2. What will be the population of the municipality after 2 years? Find it.
    3. Is the calculation process of population growth and compound interest the same? Give your opinion.
  4. The population of a village is 20,000. The population increases by 2% annually in the village.
    1. If the initial population is P, growth rate is R per annum and population after T years is PT, then write the formula to find PT.
    2. After how many years the population of population of the village will be 20,808? Find it.
    3. If the population increases at the rate of 3% per annum, By what number will the number of the village be increased in 2 Years?Find it.
  1. The population of a village is 10,000. The population grows by 2% annually.
    1. Write the formula used to find the population after T years.
    2. After how many years will the population be 10,404? Find it.
    3. If the population increases at the rate of 4% per annum, by what number will the population increase in 2 years?
  2. The population of a village is 40,000. The population grows by 5% annually.
    1. Write the formula used to find the increased population after T years.
    2. After how many years will the population be 44,100? Find it.
    3. If the population increases at the rate of 2% per annum, by what number will the population increase in 2 years?
  3. The present population of a rural municipality is 5,400. The growth rate is 2% per annum.
    1. In how many years is the population census conducted in Nepal?
    2. What will be the population after one year?
    3. If the population increases at the same rate, what will be the population after 3 years?
  4. The present population of a rural municipality is 10,000. The growth rate is 4% per annum.
    1. If the initial population is P₀ and the population after T years is Pₜ, express Pₜ in terms of P₀, T, and Q.
    2. What will be the population after one year?
    3. If the population increases at the same rate, what will be the population after 3 years?
  5. The population of Ramailo town increases by 10% every year. If the present population is 60,500:
    1. Find the population before 2 years.
    2. Compare the population before two years and after two years.
  6. The population of a town increases by 10% every year. If the present population is 48,400:
    1. Find the population before 2 years.
    2. Compare the population before two years and after two years.
  7. The population of a village is 10,000. The population increases every year by 5%. At the end of two years, the total population of the village was 10,000. Out of them, 1,025 people migrated to other places.
    1. The present population of a village is P. If the population increases by R% every year, what will be the population of the village after T years? Write it.
    2. Find the population of the village after 2 years.
    3. What was the population of the village in the beginning?
  8. The population of Ramkot village increases every year by 2.5%. At the end of two years, if 320 people migrated to other villages, the total population of the village becomes 24,895.
    1. If the initial population of any place is M₀, population after T years is Mₜ and the rate of annual population growth is R%, express Mₜ in terms of M₀, T and R.
    2. Find the population of the village after 2 years.
    3. What was the population of the village in the beginning?
  9. The population of Kathmandu valley was 2,000,000 in the beginning of the year 2077 B.S. The population growth rate was 4%. If 50,000 people were migrated there from other places in the beginning of the year 2078 B.S.
    1. What will be the population of the city in the beginning of 2078 B.S.?
    2. Find the total population in the beginning of the year 2080 B.S.
  10. In the beginning of 2077 B.S., the population of a town was 100,000 and the rate of population growth is 2% every year. If in the beginning of 2078 B.S., 8,000 people migrated there from different places,
    1. What will be the population of the city in the beginning of 2078 B.S.?
    2. Find the population of the town in the beginning of 2080 B.S.
  11. The present population of village A is 4,500 and village B is 5,000. The annual population growth rate of village A is 2%.
    1. What does P denote in the population after T years, \( P_T = P\left(1 + \frac{R}{100}\right)^T \) ? Write it.
    2. If 200 people are added by migration in village A after 1 year, what will be the population after 1 year? Find it.
    3. If the population of village B decreases by the same growth rate of village A, what will be the population of village B after 2 years? Find it.
  12. The population of a village is 10,000. The annual population growth rate is 4%. At the end of the first year, 100 people migrated from that village to other places.
    1. Find the population of the village after one year.
    2. If nobody migrated in the second year, what would be the population of the village after 2 years? Find it.
    3. If nobody migrated in the first year, what would be the difference in population growth in 2 years? Find it.
  13. The population of a city before three years was 2,500,000. The annual population growth rate of the city is 5%. One year ago, 74,000 people migrated to other places and 1,000 people died due to disease.
    1. What is the rate of annual compound growth? Write it.
    2. Find the population of the city before two years.
    3. Compare the present population and population before 3 years. Then write the conclusion.
  14. In the beginning of 2077 B.S., the population of a village was 120,000. The population growth rate of the village was 2%. In the beginning of 2079 B.S., 152 people were migrated there from other places.
    1. Find the population of the village in the beginning of 2079 B.S.
    2. What does R represent in the population after T years PT = P (1 − R / 100)T? Write it.
    3. If the population of the village was depreciated from the beginning of 2079 B.S. to the end of 2080 B.S. at the rate of 2%, what effect can you see in the population of that village during these 4 years? Write with calculation.
  15. The population of a village increases every year by 5%. At the end of two years, the total population of the village was 10,000. Out of them, 1,025 people were migrated to other places.
    1. If the initial population of any place is M₀ and the annual rate of population growth is R% per annum, what will be the population of that place after N years? Write it.
    2. Write the population after 2 years.
    3. Find the population before 2 years.
    4. What percent of population is increased in four years?
  16. The population of a town increases every year by 10%. At the end of two years, the total population of the town was 30,000. This includes 5,800 people who were added by migration.
    1. In usual notation, what does P [ (1 + R / 100)T − 1 ] stand for?
  17. In the beginning of 2075 B.S., the population of a town was 100,000 and the rate of population growth was 2% every year. In the beginning of 2076 B.S., 8,000 people migrated there from different places.
    1. Compute the population at the beginning of 2076 B.S.
    2. Find the population at the end of 2076 B.S.
    3. Identify the population at the beginning of 2078 B.S.
    4. Analyse the simple population growth of the town over the past 3 years.
  18. Three years ago, a district had a population of 375,000 and the annual population growth rate was 2%. In the second year, 1,480 people migrated in and 9,850 people died due to an epidemic.
    1. Compute the population at the end of the second year.
    2. Find the present population of the district.
    3. Analyse the simple population growth of the district over the past 3 years.
  19. The population of a municipality in 2072 was 100,000 and the annual population growth rate was 4%. In the beginning of 2073, 16,000 people migrated there from other places.
    1. Find the total population in the beginning of 2073.
    2. What was the population in the beginning of 2075?
    3. If there was no migration in the beginning of 2073, what would be the difference in population in the beginning of 2075? Find it.
  20. The population of a municipality in 2077 was 400,000 and the annual population growth rate was 5%. In the beginning of 2078, 30,000 people migrated there from other places.
    1. Find the total population in the beginning of 2078.
    2. What was the population in the beginning of 2080?
    3. If there was no migration in the beginning of 2078, what would be the difference in population in the beginning of 2080? Find it.
  21. In 2077 B.S., there were 1,000 students in a school. A rule that a group of 100 students should bring 10 new students was imposed to increase the number of students.
    1. What is the rate of annual growth of students to increase the number of students?
    2. What was the number of students in the school in 2079 B.S.? Find it.
    3. Will the number of students of the school be 1,600 in 2082 B.S.? Justify with calculation.
  22. In 2078 B.S., there were 2,000 students in a school. A rule that a group of 100 students should bring 20 new students for enrolment was imposed to increase the number of students.
    1. What is the rate of annual growth of students?
    2. What was the number of students in the school in 2080 B.S.? Find it.
    3. Will the total number of students of the school be 4,976 in 2083 B.S.? Justify with calculation.
  23. Three years ago, there were 1,000 students in a secondary school. Since the past three years, the rule “a group of 5 students should bring one new student for enrolment” was imposed to increase the number of students.
    1. Find the annual growth rate of the number of students.
    2. What is the number of students at present?
    3. Compare the number of new students in the second year and the new students in the third year.
  24. Three years ago, there were 2,000 students in a secondary school. Since the past three years, the rule “a group of 10 students should bring one new student for enrolment” was imposed to increase the number of students.
    1. Find the annual growth rate of the number of students.
    2. What is the number of students at present?
    3. Compare the number of new students in the second year and the new students in the third year.
  25. 24,000 blood donors were registered with a charitable hospital. The number of donors increases at the rate of 1/10 every year.
    1. Find the annual growth rate of blood donors.
    2. What will be the number of blood donors after two years?
    3. Find the time period at the end of which the total number of blood donors becomes 31,944.
  26. 40,000 students were registered in a university. The number of students increased at the rate of 0.05 every year.
    1. Find the annual growth rate of the number of students.
    2. What will be the number of students after two years?
    3. Find the time period at the end of which the total number of students becomes 46,305.
  27. The population of a town at the end of the year 2013 A.D. was 150,000. If the population increases during the next three years at the rate of 5%, 6% and 4% respectively,
    1. Find the population of the town at the end of 2015 A.D.
    2. What will be the population of the town at the end of 2016 A.D.?
  28. The population of a town at the end of the year 2013 A.D. was 2,000,000. If the population increases during the next three years at the rate of 4%, 5% and 10% respectively,
    1. Find the population of the town at the end of 2015 A.D.
    2. What will be the population of the town at the end of 2016 A.D.?
    3. If the population of the town had increased by 8% per annum in all the three years, how much more would the population be?
  29. The present population of a town is 177,366. If it had increased by 3%, 2.5% and 5% in the last three years,
    1. If the population growth rates of a certain place for the first three years are R1%, R2% and R3%, write the formula to calculate the population after 3 years.
    2. What was the population of the town before 1 year?
    3. Find the population of the town before three years.
    4. If the population had increased by 10% every year, how much more would the present population be?
  30. The present population of a town is 886,830. If it had increased by 3%, 2.5% and 5% in the last three years,
    1. If the population growth rates of a village for the first three years are R1%, R2% and R3%, write the formula to calculate the population after 3 years.
    2. What was the population of the town before 1 year?
    3. Find the population of the town before three years.
    4. If the population had increased by 10% every year, how much more would the present population be?
  31. The population of a colony increases from 80,000 to 92,610 at a growth rate of 5% per year after a certain period of time.
    1. Find the period of time.
    2. If the growth rate is 2% less than before, what would be the difference in population for the same time? Calculate it.
  32. The population of a colony increases from 100,000 to 172,800 at a growth rate of 20% per year after a certain period of time.
    1. Find the period of time.
    2. If the growth rate is 10% less than before, what would be the difference in population for the same time? Calculate it.
  33. According to the Co-operative Act of Nepal, the depreciation rates of office items are:
    Electronic items: 10%
    Furniture: 15%

    If the co-operative institution has the value of a computer as Rs 60,000 and a steel cabinet as Rs 15,000 in the beginning of 2076 B.S.,
    1. What do you understand by 10% price depreciation?
    2. What was the price of the computer at the end of 2078 B.S.?
    3. Find the price of the furniture at the beginning of 2079 B.S.
    4. From the beginning of 2076 B.S. to the end of 2078 B.S., show that there is a 29.31% decline in the aggregate price.
  34. According to the Co-operative Act of Nepal, the depreciation rates of office items are:
    Electronic items: 10%
    Furniture: 15%

    If the co-operative institution has the value of a laptop as Rs 80,000 and an office table as Rs 20,000 in the beginning of 2076 B.S.,
    1. What do you understand by 15% price depreciation?
    2. What was the price of the laptop at the end of 2078 B.S.?
    3. Find the price of the office table at the beginning of 2079 B.S.
    4. From the beginning of 2076 B.S. to the end of 2078 B.S., show that there is a 29.31% decline in the aggregate price.
  35. A minibus is purchased for Rs 40,00,000. After using it for three years, Rs 15,00,000 is earned. The value of the bus depreciates at the rate of 15% per annum and the minibus is sold after three years.
    1. If the purchasing price of the bus is Rs V0, the annual rate of compound depreciation is R%, and the price after T years is Rs VT, express VT in terms of V0, R% and T.
    2. Find the selling price of the bus after three years.
    3. Find the total profit or loss percent from the whole transaction.
  36. A taxi is purchased for Rs 20,00,000. After using it for three years, Rs 9,00,000 is earned. The value of the taxi depreciates at the rate of 20% per annum and the taxi is sold after three years.
    1. Find the selling price of the taxi after three years.
    2. Find the total profit or loss percent on selling the taxi.
  37. A factory established with an investment of Rs 4 crore earns Rs 75 lakhs as profit in three years. Its cost depreciates at the rate of 2.5% per annum during this period and it is sold.
    1. In usual notation, what does P − P(1 − R/100)T stand for?
    2. What will be the price of the factory after 3 years?
    3. Find it loss or gain in the whole duration
  38. A poultry farm was established 2 years ago with an investment of Rs 3,00,000. During this time, the owner gained Rs 1,50,000. Due to bird-flu disease, its cost was depreciated at the rate of 10% and the farm was sold.
    1. If PT is the price after T years, P is the initial price, R is the depreciation rate and T is time, write the relation among P, T, R and PT.
    2. Find the present price of the farm.
    3. Calculate the total gain or loss for the owner during the period.
  39. Neelam bought a machine for Rs 40,000. The price of the machine depreciates at the rate of 5% per annum. The machine was sold for Rs 36,100 after using it for some years.
    1. By how much does the price of the machine depreciate in the first year?
    2. After how many years was the machine sold?
    3. Find the profit or loss percentage from selling the machine if she earns Rs 4,900 from renting the machine.
  40. An electric bus was purchased for Rs 45,00,000. Using the bus for 2 years, Rs 12,00,000 was earned. The value of the bus depreciates at the rate of 10% per annum.
    1. If the initial price of the bus is V0, the annual rate of depreciation is R and the price after T years is VT, express VT in terms of V0, R and T.
    2. How much does the price of the bus depreciate in the first year?
    3. If the bus is sold after 2 years, what will be the percentage of profit or loss?
  41. A photocopy machine was purchased for Rs 80,000. After using it for 2 years, only Rs 30,000 was earned. The price of the machine depreciates annually at the rate of 20% and the machine was sold after 2 years.
    1. If the initial price of a machine is V0, annual rate of compound depreciation is R and the price after T years is VT, express VT in terms of V0, R and T.
    2. Find the total profit or loss amount on selling the machine.
    3. If the machine had been sold after using it one more year, by how much would the selling price be less than the purchasing price? Compare it.
  42. Furba bought a tractor for Rs 7,20,000. He earned Rs 2,20,000 in 3 years from it and sold it at a price which depreciates at the rate of 10% per annum.
    1. Which formula is used to calculate the price after 3 years?
    2. Identify the price after 3 years.
    3. Find the price depreciation amount in 3 years
    4. Goverment have provided him interest free loan to buy the tracktor. In this context what is his profit or loss in 3 years
  43. Suman bought a taxi for Rs 8,00,000. He earned Rs 2,50,000 in 3 years from it and sold it at a price depreciated at the rate of 10% per annum.
    1. Which formula is used to calculate the depreciated price in 3 years?
    2. Identify the price after 3 years.
    3. Find the price depreciation amount in 3 years.
    4. The government provided him an interest-free loan to buy the taxi. In this context, what is his profit or loss in 3 years?
  44. A person purchased some shares of a hydropower company. The value of the shares depreciated at the rate of 10% for 2 years and the person sold his shares entirely at the end of 2 years for Rs 25,920.
    1. How much amount was invested for buying the shares?
    2. What percentage of loss did he bear on his investment?
    3. If the person had sold his shares after an increment of 8% per year for 2 years, how much would he have gained?
  45. A person purchased some shares of a hydropower company. The value of the shares depreciated at the rate of 10% for 2 years and the person sold his shares entirely at the end of 2 years for Rs 40,500.
    1. How much amount was invested for buying the shares?
    2. What percentage of loss did he bear on his investment?
    3. If the person had sold his shares after an increment of 8% per year for 2 years, how much would he have gained?
  46. A man bought a computer for Rs 44,100 and after using it for 2 years, he sold it for Rs 40,000.
    1. Find the compound depreciation amount in 2 years.
    2. Compute the rate of compound depreciation of the computer.
    3. If the depreciation rate was 10%, then by what percentage would the price be less or more after 2 years?
  47. A man bought a motorcycle for Rs 96,100 and after using it for 2 years, he sold it for Rs 90,000.
    1. Compute the compound depreciation amount in 2 years.
    2. Find the rate of compound depreciation of the motorcycle.
    3. If the depreciation rate was 10%, then by what percentage would the price be less or more after 2 years?
  48. The present price of a car is Rs 20,00,000. If its price reduces by 10% annually,
    1. Identify the price after 1 year.
    2. After how many years will its price be Rs 14,58,000? Find it.
    3. At what annual depreciation rate should the price of the car be depreciated to get Rs 10,24,000 after 3 years?
  49. The present price of a television is Rs 35,000. If its price reduces by 10% per annum,
    1. Identify the price after 1 year.
    2. After how many years will the price be Rs 25,515? Find it.
    3. At what annual depreciation rate should the price of the television be depreciated to get Rs 17,920 after 3 years?
  50. The present price of a machine is Rs 5,00,000. If the price of the machine depreciates by 15% in the first year and then by 10% and 5% respectively in the following years,
    1. Find the price of the machine after 1 year.
    2. What will be the price of the machine after 3 years?
    3. If the price was depreciated by 10% per annum in all the three years, then how much more or less would be the price of the machine?
  51. The present price of a machine is Rs 8,00,000. If the price of the machine depreciates by 10% in the first year and then by 8% and 5% respectively in the following years,
    1. Find the price of the machine after 1 year.
    2. What will be the price of the machine after 3 years?
    3. If the price was depreciated by 8% per annum in all the three years, then how much more or less would be the price of the machine?
  52. A machinery goods bought for Rs 1,00,000 depreciates by 10% in the first 2 years and then by 5% in the next 1 year.
    1. Find the price after 1 year.
    2. What will be its price after 3 years?
    3. If the depreciation rates of the first two years and the next one year are exchanged, what will be the difference in price after 3 years?
  53. A new Pajero costs Rs 36,00,000. Its price depreciates at the rate of 10% per year during the first two years and at the rate of 20% per year thereafter.
    1. Find the price after 1 year.
    2. What will be the price of the Pajero after 3 years?
    3. If the depreciation rates of the first two years and the next one year are exchanged, what will be the difference in price after 3 years?
  54. The cost of a TV was quoted at Rs 50,000 at the end of 2000 AD. In the beginning of 2001 AD, the price was hiked by 5%. Because of the decrease in demand, the cost was reduced by 4% in the beginning of 2002 AD.
    1. Write the formula to find compound depreciation.
    2. How much did the customer pay for the TV who bought it at the end of 2002 AD?
    3. How much more or less should the customer pay at the end of 2002 AD than at the end of 2001 AD?
  55. The initial price of a machine was Rs 5,00,000. If the price of the machine in the first year was increased by 10% and then depreciated in the following years by 5% and 4% respectively,
    1. If the depreciation rates for the first three years are R1%, R2% and R3% respectively, write the formula to calculate the depreciated price after 3 years.
    2. Compute the price of the machine at the end of the first year.
    3. Find the price of the machine at the end of the second year.
    4. If the machine is sold at the end of the third year, what is the profit or loss?
  56. The initial price of a machine was Rs 8,00,000. If the price of the machine in the first year was increased by 10% and then depreciated in the following years by 5% and 4% respectively,
    1. If the depreciation rates for the first three years are R1%, R2% and R3% respectively, write the formula to calculate the price after 3 years.
    2. Compute the price of the machine at the end of the first year.
    3. Find the price of the machine at the end of the second year.
    4. If the machine is sold at the end of the third year, what is the profit or loss?
  57. The present price of a machine is Rs 50,000. The price of the machine is depreciated at 8% per annum.
    1. What do you mean by annual compound depreciation? Write it.
    2. What will be the price of the machine after 2 years? Find it.
    3. If the price of the machine depreciates by 8% in the first year and 10% in the second year, what will be the depreciated price? Find it.
  58. The present price of a machine is Rs 80,000. The price of the machine is depreciated at 10% per annum.
    1. What will be the price of the machine after 2 years? Find it.
    2. If the price of the machine depreciates by 10% in the first year and 12% in the second year, what will be the depreciated price? Find it.
  59. A man bought a plot of land for Rs 16,00,000 and a car for Rs 18,00,000 at the same time. The price of the plot of land grows uniformly at the rate of 25% per annum while the price of the car depreciates by 20% per annum. If the man sells the plot of land as well as the car after 3 years, answer the following questions:
    1. What is the initial total investment of the person?
    2. Find the price of the land after 3 years.
    3. At what price did he sell the car after 3 years?
    4. Analyse his profit or loss in his total transaction.
  60. A man bought a plot of land for Rs 20,00,000 and a car for Rs 25,00,000 at the same time. The price of the plot of land grows uniformly at the rate of 25% per annum while the price of the car depreciates by 20% per annum. If the man sells the plot of land as well as the car after 3 years, answer the following questions:
    1. What is the initial total investment of the person?
    2. Find the price of the land after 3 years.
    3. At what price did he sell the car after 3 years?
    4. Analyse his profit or loss in his total transaction.
  61. The initial population of Rampur was 2,40,000 and that of Laxmanpur was 2,30,000. The population of Rampur increases by 4% per year and the population of Laxmanpur decreases by 5% per year.
    1. Write the formula for finding population after T years.
    2. After 2 years which place has more population and by how much? Find it.
    3. By what percentage should the population of Laxmanpur increase in 2 years to reach the same population as the initial population of Rampur? Find it.
  62. The initial population of Bharatpur was 3,95,352 and that of Janakpur was 3,80,000. The population of Bharatpur increases by 2% per year and the population of Janakpur decreases by 1% per year.
    1. After 2 years which place has more population and by how much? Find it.
    2. By what percentage should the population of Janakpur increase in 2 years to reach the same population as the initial population of Bharatpur? Find it.
  63. Sajan has Rs 1,00,00,000 with him. Sajan purchased a car for Rs 30,00,000 and land for Rs 70,00,000. For 2 years, the price of the car has been decreasing at a compound rate of 5% per annum, while the price of land has been increasing at a certain compound rate.
    1. If the initial price of an article is Rs N and the annual rate of compound depreciation is R%, then what will be the price of the article after T years? Write it.
    2. What will be the price of the car after two years? Calculate.
    3. After 2 years the total price of car and land is Rs 1,05,72,700, what is the increase compound rate in the price of land? Calculate
  64. Rajan has Rs 2,00,00,000. Rajan purchased a car for Rs 60,00,000 and land for Rs 1,40,00,000. For 2 years, the price of the car has been decreasing at a compound rate of 5% per annum, while the price of land has been increasing at a certain compound rate.
    1. What will be the price of the car after 2 years? Find it.
    2. After 2 years, if the total price of land and car is Rs 2,11,45,400, then what is the rate of compound growth in the price of land? Calculate it.
  65. Rajiv has got Rs 12,00,000. He purchased a motorcycle for Rs 2,00,000 and a land for Rs 10,00,000. The price of motorcycle has been depreciating at a compound rate of 10% per annum for 2 years, while the price of land has been increasing at the compound rate of 12% per annum.
    1. Write the formula to calculate compound growth.
    2. What will be the price of land after 2 years? Find it.
    3. Will the total price of motorcycle and land after 2 years be Rs 15,00,000? Write with calculation.
  66. The cost of a land is Rs 50,00,000 and the cost of a house is Rs 80,00,000. The cost of land increases by 10% per annum and the cost of house decreases by 20% per annum.
    1. Write the formula to find the price after T years if the initial price is Rs P and the rate of compound depreciation is R% per annum.
    2. What is the cost of house after 2 years? Find it.
    3. How much profit or loss is made from selling the land and house after 3 years? Compare it.
  67. A man bought a land at Rs 80,00,000 on 25th Baisakh of 2075 B.S. and started construction of a house on the same day. The construction of the house completed at the cost of Rs 2,70,00,000. If the price of land increased at the rate of 20% per year and the price of house decreased at the rate of 20% per year, then:
    1. What will be the price of the land after 2 years?
    2. What will be the price of the house after 2 years?
    3. Will the prices of the land and house be the same after 2 years? If not, in how many years will the prices of the land and house be equal?
  68. A man bought a land at Rs 20,00,000 on 25th Baisakh of 2075 B.S. and started construction of a house on the same day. The construction of the house completed at the cost of Rs 67,50,000. If the price of land increased at the rate of 20% per year and the price of house decreased at the rate of 20% per year, then:
    1. In a village the total number of new born babies is x, total increased population is y and total death number is z in a certain interval of time. Write the relation among x, y and z.
    2. What will be the price of land after 2 years?
    3. What will be the price of house after 2 years?
  69. The price of a piece of land in Kathmandu was fixed at Rs 60,00,000 at the end of 2020 AD. The price increased by 10% as the consequence of increasing buying pressure in the beginning of 2021. But the price of land decreased by 4% due to the economic crisis in the beginning of 2022 AD.
    1. What does P represent in P(1 + R/100)T − P as per usual notation?
    2. What will be the price of the land at the end of 2022?
    3. How much loss will be there to the person if the price decreased by 5% instead of decreasing by 4% in 2022 AD?
  70. The price of a piece of land in Pokhara was fixed at Rs 1,20,00,000 at the end of 2020 AD. The price increased by 10% as the consequence of increasing buying pressure in the beginning of 2021. But the price of land decreased by 4% due to the economic crisis in the beginning of 2022 AD.
    1. Find the price of 1 Aana land in the year 2020 AD.
    2. What will be the price of the land at the end of 2022?
    3. How much loss will be there to the person if the price decreased by 5% instead of decreasing by 4% in 2022 AD?
  71. The price of a land before 3 years was Rs 32,00,000 per Ropani. It was depreciated by 10% per annum for first 2 years. In the third year its value is increased by 20%.
    1. Which formulae are used for value depreciation and value increment? Write the meaning of each symbol.
    2. What was the price of 1 Aana land before 1 year? Compute it.
    3. What is the price of 4 Aana land now? Find it.
    4. Analyse the price of the land over the past 3 years.
  72. Three years ago a company bought 5 Ropani of land at Rs 2,80,000. Due to the political instability of the country the price of the land is depreciated. If the price of the land is depreciated at 5% per annum:
    1. Find the price of 1 Ropani land before 3 years.
    2. What is the price of the land per Ropani? Compute it.
    3. What is the present value of 5 Ropani land?
    4. What would be the profit if the company had deposited the money at annual compound interest rate of 10% instead of purchasing land?
  73. Ramesh purchased a residential home which was constructed in a land of 7 Aana in Kathmandu. The price of the land was Rs 80,00,000 and the price of the house was Rs 1,56,25,000. If the value of the house depreciates every year by 12% and the value of the land increases every year by 10% (compounded annually), answer the following questions.
    1. If P = Initial population, D = Number of deaths at the end and Min = Number of migrants entered after T years then write the formula to calculate the population after T years.
    2. What will be the value of the land in 2 years?
    3. What will be the value of the house in 2 years?
    4. In how many years will the value of the land and the value of the house be equal?
  74. Ramesh purchased a residential home which was constructed in a land of 7 Aana in Dharan. The price of the land was Rs 40,00,000 and the price of the house was Rs 78,12,500. If the value of the house depreciates every year by 12% and the value of the land increases every year by 10% (compounded annually), answer the following questions.
    1. If P = Initial population, D = Number of deaths, Min = Number of migrants entered and Mout = Number of migrants left after T years then write the formula to calculate the population after T years.
    2. What will be the value of the land in 2 years?
    3. What will be the value of the house in 2 years?
    4. In how many years will the value of the land and the value of the house be equal?
  75. Ganesh purchased an industrial land at Rs 1,60,00,000 and a printing machine at Rs 5,40,00,000. If the value of the land increases at 20% per annum and the value of the machine depreciates at 20% per annum (compounded annually):
    1. Define compound growth of price.
    2. What will be the value of the land after 2 years?
    3. What will be the value of the machine after 2 years?
    4. In how many years will the value of the machine and the value of the land be equal?
  76. Hridesh purchased an industrial land at Rs 32,00,000 and a printing machine at Rs 1,08,00,000. If the value of the land increases at 20% per annum and the value of the machine depreciates at 20% per annum (compounded annually):
    1. Define compound price depreciation.
    2. What will be the value of the land after 2 years?
    3. What will be the value of the machine after 2 years?
    4. In how many years will the value of the machine and the value of the land be equal?
  77. The price of a motorcycle depreciates by 12% every year. A man pays Rs 5,00,000 for his motorcycle.
    1. Identify the price of the motorcycle after 2 years.
    2. What will be the price depreciation of the motorcycle in 2 years?
    3. If the person had bought the motorcycle by taking a loan at 10% per annum compounded annually and decided to pay off the motorcycle loan after two years by selling it, how much additional money does he need?
  78. The price of a car depreciates by 15% every year. A man pays Rs 20,00,000 for his car.
    1. What will be the price of the car after 2 years?
    2. Compute the price depreciation of the car in 2 years.
    3. If the person had bought the car by taking a loan at 10% per annum compounded annually and decided to pay off the car loan after two years by selling it, how much additional money does he need?

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