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Quiz: Compound Interest

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Number of Questions: 30

Question: 21 -

900 workers were employed to construct a dam in four years. At the end of first year, 5% workers were retrenched. At the end of the second year 2% of the workers were retrenched. To complete the construction in time, the number of workers were increased to 10% at the end of third year. How many workers were working at the end of fourth year.

Options:

  1. 945

  2. 1000

  3. 989

  4. 921

    5. Answer:

    921
    Solution:

    Initial number of workers = 900
    Reduction of workers at the end of first year = 5%
    Reduction of workers at the end of second year = 2%
    Increase of workers at the end third year = 10%
    Number of workers working during fourth year = 900 (1 – 5/100)(1 – 2/100)(1 + 10/100)
    = 900 (95/100)(98/100)(110/100) = 921.69 ≅ 921 workers.

Question: 22 -

Two years ago the population of a village was 4000. If the annual increase during the two successive years be at the rate of 2% & 4%, find the present population.

Options:

  1. 7072

  2. 7080

  3. 7074

  4. 7000

    5. Answer:

    7072
    Solution:

    Present population = 4000 (1 + 2/100)(1 + 4/100) = 4000 (51/50)(26/25) = 7072.

Question: 23 -

Smith started a business with initial investment of 500000. He incurred a loss of 2% in the first year and in the second year he gained the profit of 10%. Calculate his net profit earned.

Options:

  1. 39000

  2. 40000

  3. 41000

  4. 38000

    5. Answer:

    39000
    Solution:

    Initial investment = 500000
    Profit = 500000 (1 – 2/100)(1 + 10/100) = 500000 (49/50)(11/10) = 539000
    ⇒ Net profit earned = 500000 – 539000 = 39000.

Question: 24 -

Ajay opened a cafe with an initial investment of Rs. 64000. In the first year he incurred the loss of 10%. During second year he gained the profit of 4% and in the third year he gained the profit of 15%. Calculate his net profit gained in the entire three years.

Options:

  1. 68889.5

  2. 68889.61

  3. 4889.6

  4. 68889.60

    5. Answer:

    4889.6
    Solution:

    Initial investment = Rs. 64000
    Loss in first year = 10%
    Profit in second year = 4%
    Profit in third year = 15%
    profit = 64000 (1 – 10/100)(1 + 4/100)(1 + 15/100) = 64000 (9/10)(26/25)(23/20) = 68889.60.
    Net profit = 68889.60 – 64000 = 4889.6.

Question: 25 -

A company increased the production of cars from 15625 in 2002 to 27000 in 2005. Find the annual rate of growth of production of the cars.

Options:

  1. 2%

  2. 10%

  3. 15%

  4. 20%

    5. Answer:

    20%
    Solution:

    Let the annual rate of growth be R% per annum. Then,
    ⇒ 27000 = 15625 (1 + R/100)3
    ⇒ 27000/15625 = (1 + R/100)3
    ⇒ (30/25)3 = (1 + R/100)3
    ⇒ 30/25 = 1 + R/100
    ⇒ 1/5 = R/100
    ⇒ R = 20%.