Discount


  1. If a commission of 10% is given on the written price of an article, the gain is 20%. The gain per cent, when the commission is increased to 20%, will be ?
    1. 62/3%
    2. 5%
    3. 8%
    4. 51/3%

  1. View Hint View Answer Discuss in Forum

    Let MP of the article = ₹ N
    ∴ SP of the article = N x (100 - 10)/100 = ₹ 9N/10
    ⇒ CP of the article = [(9N/10) x 100]/(100 + 20)
    = (9N x 10)/120
    = ₹ 3N/4

    Now, new SP of the article = [N x (100 - 20)]/100 = ₹ 4N/5
    New profit = 4N/5 - 3N/4 = (16N - 15N)/20 = ₹ N/20
    Hence, profit per cent = [(N/20) / (3N/4)] x 100 %

    Correct Option: A

    Let MP of the article = ₹ N
    ∴ SP of the article = N x (100 - 10)/100 = ₹ 9N/10
    ⇒ CP of the article = [(9N/10) x 100]/(100 + 20)
    = (9N x 10)/120
    = ₹ 3N/4

    Now, new SP of the article = [N x (100 - 20)]/100 = ₹ 4N/5
    New profit = 4N/5 - 3N/4 = (16N - 15N)/20 = ₹ N/20
    Hence, profit per cent = [(N/20) / (3N/4)] x 100 %
    = (4 x 100)/(3 x 20) %
    = 62/3%


  1. If the discount on a certain sum in 2 years at a certain rate is $ 150 and the interest in 3 years is $ 240. Find the sum and the rate of interest.
    1. $ 2400, 31%
      3
    2. $ 2400, 41%
      3
    3. $ 2200, 51%
      3
    4. $ 2000, 31%
      3
    5. None of these

  1. View Hint View Answer Discuss in Forum

    Given :- Interest for 3 years = $ 240.

    Interest for 2 year =240 × 2= $160
    3

    Banker 's Discount = $160
    Discount for 2 years = $150
    True Discount = $150

    Sum due =Banker 's Discount × True Discount=160 × 150= $ 2400
    Banker 's Discount - True Discount160 - 150

    Rate of interest =Interest × 100%
    Sum due × Time

    Correct Option: A

    Given :- Interest for 3 years = $ 240.

    Interest for 2 year =240 × 2= $160
    3

    Banker 's Discount = $160
    Discount for 2 years = $150
    True Discount = $150

    Sum due =Banker 's Discount × True Discount=160 × 150= $ 2400
    Banker 's Discount - True Discount160 - 150

    Rate of interest =Interest × 100%
    Sum due × Time

    Rate of interest =240 × 100= 31%
    2400 × 33



  1. A bill which being due at the end of 4 years is now worth $ 575, but if it is due in 2 years 6 months, it would now be worth $ 620. The sum of the bill is :
    1. $ 695
    2. $ 725
    3. $ 713
    4. None of these

  1. View Hint View Answer Discuss in Forum

    Let, the rate p.c. be r%.
    Given :- Present worth = $ 575 and Time = 4 years
    Let, $ x be the amount of the bill.

    ∴ Present worth = Amount x Rate x Time
    100 + Rate x Time

    Then, 575 =
    x × 100
    100 + 4r

    That is, 57500 + 2300r = 100x
    ∴ x = 575 + 23r …(1)
    Present worth = $ 620 and Time = 2 years and 6 months = 2.5 years
    and 620 =
    100x
    100 + 2.5 r

    Correct Option: C

    Let, the rate p.c. be r%.
    Given :- Present worth = $ 575 and Time = 4 years
    Let, $ x be the amount of the bill.

    ∴ Present worth = Amount x Rate x Time
    100 + Rate x Time

    Then, 575 =
    x × 100
    100 + 4r

    That is, 57500 + 2300r = 100x
    ∴ x = 575 + 23r …(1)
    Present worth = $ 620 and Time = 2 years and 6 months = 2.5 years
    and 620 =
    100x
    100 + 2.5 r

    ∴ 62000 + 1550r = 100x
    ∴ 6200 + 155r = 10x = 5750 + 230r [using (1)]
    ∴ 75r = 450
    ∴ r = 6
    Putting the value of x in eq. (1) ⇒ x = 575 + 138 = $ 713.
    Hence , The sum of the bill is $ 713.


  1. Find the present worth (P.W.) and the true discount reckoning 6 % per annum simple interest of $ 176 due in 20 months time.
    1. $ 160, $ 16
    2. $ 130, $ 46
    3. $ 150, $ 26
    4. None of these

  1. View Hint View Answer Discuss in Forum

    Here , simple interest = $ 176 , Rate = 6% , Time = 20 months = ( 20/12 ) years

    ∴ Present worth = Simple interest x Rate x Time
    100 + Rate x Time

    Present worth =100 x 76
    100 + [ 2 x ( 20/12 ) ]

    Correct Option: A

    Here , simple interest = $ 176 , Rate = 6% , Time = 20 months = ( 20/12 ) years

    Present worth =100 x 76
    100 + [ 2 x ( 20/12 ) ]

    Present worth =100 x 76= $ 160
    100 + 10

    True discount = Amount - Present worth
    True discount = $ 176 - $ 160 = $ 16.



  1. The discount on $ 5229 due in 1 year 9 months reckoning compound interest at 5 % is :
    1. $ 429.00
    2. $ 415.00
    3. $ 393.25
    4. None of these

  1. View Hint View Answer Discuss in Forum

    P.W =
    5229
    [(1 + 5 / 100)][1 + (3 / 4)(5 / 100)]

    Correct Option: A

    P.W =
    5229
    [(1 + 5 / 100)][1 + (3 / 4)(5 / 100)]

    = 5229 x 20x 80= $ 4800
    2183

    ∴ T.D. = $ (5229 - 4800) = $ 429.