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Simple Interest Exercise 2

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  1. Question 1 of 20
    1. Question

    A man received Rs 12000 as Puja Bonus. He invested a part of it at 5% per annum and the remaining at 6% per annum on simple interest being allowed in each case. The total interest earned by him in 4 years is Rs 2580. The sum invested at 5% per annum is

    Hint

    Let the sum invested at 5% be Rs x.

    According to the question,

    interest-32441.png

    = 2580

    interest-32435.png

    interest-32429.png

    interest-32423.png

    ⇒ x = Rs 7500.

  2. Question 2 of 20
    2. Question

    The simple interest accrued on a sum of certain principal is Rs 1,200 in four year at the rate of 8% p.a. What would be the simple interest accrued on thrice of that principal at the rate of 6% p.a in 3 year?

    Hint

    Principal

    = interest-34597.png

    = Rs 3750

    Simple interest on thrice that principal

    = interest-34591.png

    = Rs 2025

  3. Question 3 of 20
    3. Question

    Mr. Sane invested a total amount of Rs 16,500 for two years in two schemes A and B with rate of simple interest 10 p.c.p.a. and 12 p.c.p.a. respectively. If the total amount of interest earned was Rs 3,620, what was the amount invested in scheme B?

    Hint

    % interest on total amount per annum

    = interest-34585.png

    Now, use Alligation method.

    interest-34579.png

    Hence, ratio of amount invested in schemes A and B

    = interest-34572.png

    Hence, amount invested in B

    =interest-34566.png= Rs 8000

  4. Question 4 of 20
    4. Question

    Out of a certain sum, ⅓rd is invested at 3%, ⅙th at 6% and the rest at 8%. If the simple interest for 2 years from all these investments amounts to Rs 600, find the original sum.

    Hint

    Rest part

    interest-34560.png

    Rate % per annum on total sum

    interest-34554.png

    ∴ interest-34548.png

  5. Question 5 of 20
    5. Question

    The simple interest on a sum of money is ¹⁄₉ of the principal and the number of years is equal to the rate % p.a. The rate % p.a. is

    Hint

    Here interest-34542.pngand R = T

    interest-34536.png

    interest-34530.png

  6. Question 6 of 20
    6. Question

    A sum of money lent out at simple interest amounts to Rs 720 after 2 years and to Rs 1,020 after a further period of 5 years. Find the sum and the rate %.

    Hint

    S.I. for 5 years

    = Rs (1020 –720) = Rs 300

    SI. for 2 years

    = interest-34512.png

    ∴ Principal = Rs (720 – 120) = Rs 600

    Now, P = 600, T = 2, S.I. = 120

    ∴ interest-34506.png

  7. Question 7 of 20
    7. Question

    A sum was put at simple interest at a certain rate for 4 years Had it been put at 2% higher rate, it would have fetched Rs 56 more. Find the sum.

    Hint

    Difference in S.I.

    interest-34499.png

    ⇒ interest-34493.png (Since R₁ – R₂ = 2)

    ⇒ interest-34487.png

  8. Question 8 of 20
    8. Question

    Adam borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond five years. If he pays a total interest of Rs 11,400 at the end of nine years, how much money did he borrow?

    Hint

    Let the sum borrowed be x. Then,

    interest-34481.png

    interest-34475.png

    interest-34468.png

    Hence, sum borrowed = Rs 12,000.

  9. Question 9 of 20
    9. Question

    Two equal sums of money were invested, one at 4% and the other at 4.5%. At the end of 7 years, the simple interest received from the latter exceeded to that received from the former by Rs 31.50. Each sum was :

    Hint

    Difference of S.I.

    = interest-34462.png

    Let each sum be Rs x. Then

    interest-34456.png

    ⇒ interest-34450.png

    ⇒ x = Rs 900

  10. Question 10 of 20
    10. Question

    A sum of Rs 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs 362.50 more is lent but at the rate twice the former. At the end of the year, Rs 33.50 is earned as interest from both the loans. What was the original rate of interest?

    Hint

    Let the original rate be R%.

    Then, new rate = (2R)%.

    interest-34444.png

    interest-34438.png

    interest-34432.png

  11. Question 11 of 20
    11. Question

    A father left a will of Rs 68,000 to be divided between his two sons aged 10 years and 12 years such that they may get equal amount when each attains the age of 18 years If the money is reckoned at 10% p.a., find how much each gets at the time of the will.

    Hint

    Let one gets = Rs x,

    then, second gets = Rs (68,000 – x)

    Given : A₁ = A₂

    interest-34426.png

    interest-34418.png

    interest-34412.png

    interest-34406.png

    ∴ second gets = Rs 36,000

  12. Question 12 of 20
    12. Question

    If there are three sum of money P,Q and R so that P is the simple interest of Q and Q is the simple interest of R, rate % and time are same in each case, then the relation of P, Q and R is given by

    Hint

    interest-32490.png

    interest-32484.png

    ∴ Q² = PR.

  13. Question 13 of 20
    13. Question

    A milk man borrowed Rs 2,500 from two money lendeRs For one loan, he paid 5% p.a. and for the other, he paid 7% p.a. The total interest paid for two years was Rs 275. How much did he borrow at 7% rate?

    Hint

    Let he borrowed at 5% = Rs x

    ∴ He borrowed at 7% = Rs (2500 – x)

    Now I₁ + I₂ = 275

    interest-32700.png

    ⇒ 10x + 14 (2500 – x) = 27500

    ⇒ 4x = 35000 – 27500 = 7500

    ⇒ x = Rs 1875

    ∴ Sum borrowed at 7% rate

    = 2500 – 1875 = Rs 625

  14. Question 14 of 20
    14. Question

    Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years If the total interest paid by him at the end of eleven years is Rs 8160, how much money did he borrow?

    Hint

    Let the sum be Rs x. Then,

    interest-32694.png

    ⇒ 18 x + 45x + 39x = (8160 × 100)

    ⇒ 102x = 816000

    ⇒ x = 8000.

  15. Question 15 of 20
    15. Question

    Mr. Thomas invested an amount of Rs 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs 3508, what was the amount invested in Scheme B?

    Hint

    Let the sum invested in Scheme A be Rs x and that in Scheme B be Rs (13900 – x).

    Then, interest-32688.png

    ⇒ 28x – 22x = 350800 – (13900 × 22)

    ⇒ 6x = 45000

    ⇒ x = 7500.

    So, sum invested in Scheme B

    = Rs (13900 – 7500) = Rs 6400.

  16. Question 16 of 20
    16. Question

    An amount of Rs 1,00,000 is invested in two types of shares. The first yields an interest of 9% p.a. and the second, 11% p.a. If the total interest at the end of one year is 9¾% , then the amount invested in each share was:

    Hint

    Let the sum invested at 9% be Rs x and that invested at 11% be Rs (100000 – x).

    Then, interest-32682.pnginterest-32676.png

    interest-32670.png

    ⇒ 2x = (1100000 – 975000) = 125000

    ⇒ x = 62500.

    ∴ Sum invested at 9% = Rs 62500.

    Sum invested at 11%

    = Rs (100000 – 62500) = Rs 37500.

  17. Question 17 of 20
    17. Question

    David invested certain amount in three different Schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the total interest accrued in one year was Rs 3200 and the amount invested in Scheme C was 150 % of the amount invested in Scheme A and 240% of the amount invested in Scheme B, what was the amount invested in Scheme B?

    Hint

    Let x, y and z be the amounts invested in schemes A, B and C respectively. Then,

    interest-32664.png

    ⇒ 10x + 12y + 15z = 320000 … (i)

    Now, z = 240% of y

    = interest-32658.png … (ii)

    And, z = 150% of x

    = interest-32652.png

    interest-32646.png … (iii)

    From (i), (ii) and (iii), we have :

    16y + 12y + 36y = 320000

    ⇒ 64y = 320000

    ⇒ y = 5000.

    ∴ Sum invested in Scheme B = Rs 5000.

  18. Question 18 of 20
    18. Question

    Rajesh gave Rs 1200 on loan. Some amount he gave at 4% per annum simple interest and remaining at 5% per annum simple interest. After two years, he got Rs 110 as interest. Then the amounts given at 4% and 5% per annum simple interest are, respectively :

    Hint

    Let the amount of the loss at 4% per annum be Rs x.

    Amount given at 5% per annum = Rs (1200 – x)

    Now, interest-32603.png

    ⇒ x = Rs 500

    And, (1200 – x)

    = 1200 – 500 = Rs 700

  19. Question 19 of 20
    19. Question

    Divide Rs 2379 into 3 parts so that their amounts after 2, 3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is:

    Hint

    Let the parts be x, y and [2379 – (x + y)].

    interest-32597.png

    interest-32591.png

    interest-32585.png

    But x + y +z = 2379.

    interest-32579.png

    ⇒ 1380 k + 1320 k + 1256 k

    = 2379 × 11 × 23 × 6

    interest-32573.png

    interest-32567.png

    Hence, the first part is Rs 828.

  20. Question 20 of 20
    20. Question

    Simple interest on a certain amount is ⁹⁄₁₆ of the principal. If the numbers representing the rate of interest in percent and time in years be equal, then time, for which the principal is lent out, is:

    Hint

    interest-33190.png

    interest-33184.png

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