Profit and Loss


  1. A fruit-seller buys some oranges and by selling 40% of them he realises the cost price of all the oranges. As the oranges being to grow over-ripe, he reduces the price and sells 80% of the remaining oranges at half the previous rate of profit. The rest of the oranges being rotten are thrown away. The overall percentage of profit is









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    Let Number of oranges bought = 100
    And C.P. of oranges = $ 100
    S.P of 40 oranges = $ 100
    Gain on 40 Oranges = 100 - 40 = $ 60

    ∴ Gain percent =
    60
    × 100 = 150 %
    40

    Remaining oranges = 60
    Their 80 % =
    60 × 80
    = 48
    100

    Correct Option: B

    Let Number of oranges bought = 100
    And C.P. of oranges = $ 100
    S.P of 40 oranges = $ 100
    Gain on 40 Oranges = 100 - 40 = $ 60

    ∴ Gain percent =
    60
    × 100 = 150 %
    40

    Remaining oranges = 60
    Their 80 % =
    60 × 80
    = 48
    100

    These are sold at a profit of 75 % .
    ∴ Their S.P. =
    48 × 175
    = $ 84
    100

    12 oranges was rotten so he threw away.
    ∴ Total SP = 100 + 84 = $ 184
    Gain = Total SP - CP = 184 - 100 = $ 84
    ∴ Gain percent =
    84
    × 100 = 84%
    100


  1. A shop-keeper sold a sewing machine for $ 1,080 at a loss of 10%. At what price should he has to sold it so as to gain 10% on it ? (in $ )









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    Here , Selling Price of sewing machine = $ 1080
    at a loss of 10% ,

    Cost price of sewing machine = 1080 ×
    100
    = $1200
    90

    Correct Option: D

    Here , Selling Price of sewing machine = $ 1080
    at a loss of 10% ,

    Cost price of sewing machine = 1080 ×
    100
    = $1200
    90

    ∴ S.P. for a profit of 10% =
    1200 × 110
    = $1320
    100



  1. If I purchased 11 books for $ 100 and sold 10 books for $ 110, the percentage of profit per book sold is









  1. View Hint View Answer Discuss in Forum

    If a articles are bought for $ p
    and b articles are sold for $ q,
    then

    Gain% = qa - pb× 100
    pb

    Gain% = 11 × 110 - 10 × 100 × 100
    10 × 100

    Gain % =
    1210 - 1000
    × 100 = 21%
    1000

    Second method to solve this question :
    Here, a = 11, p = 100 and b = 10, y = 110
    Gain% = aq - bp × 100%
    bp

    Correct Option: D

    If a articles are bought for $ p
    and b articles are sold for $ q,
    then

    Gain% = qa - pb× 100
    pb

    Gain% = 11 × 110 - 10 × 100 × 100
    10 × 100

    Gain % =
    1210 - 1000
    × 100 = 21%
    1000

    Second method to solve this question :
    Here, a = 11, p = 100 and b = 10, y = 110
    Gain% = aq - bp × 100%
    bp

    Gain% = 11 × 110 - 10 × 100 × 100
    10 × 100

    Gain% =
    1210 - 1000
    × 100% = 21%
    1000



  1. A vendor sells lemons at the rate of 5 for $ 14, gaining thereby 40%. For how much did he buy a dozen lemons?









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    Given that , S.P. of 5 lemons = $ 14
    On gain 40% ,

    C.P. of 5 lemons =
    100
    × 14 = $ 10
    140

    ∴ C.P. of 12 lemons =
    10
    × 21 = $ 24
    5

    We can find required answer with the help of given formula :
    Here, a = 12, p = ? and b = 5, q = 14, Gain% = 40%
    Gain% = aq - bp× 100%
    bp

    Correct Option: C

    Given that , S.P. of 5 lemons = $ 14
    On gain 40% ,

    C.P. of 5 lemons =
    100
    × 14 = $ 10
    140

    ∴ C.P. of 12 lemons =
    10
    × 21 = $ 24
    5

    We can find required answer with the help of given formula :
    Here, a = 12, p = ? and b = 5, q = 14, Gain% = 40%
    Gain% = aq - bp× 100%
    bp

    40% = 12 × 14 - 5 × p × 100%
    5p

    ⇒ 2p = 168 – 5p
    ⇒ 7p = 168
    ⇒ p = 24



  1. A person bought 50 pens for $ 50 each. He sold 40 of them at a loss of 5%. He wants to gain 10% on the whole. Then his gain per cent on the remaining pens should be









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    Here , C.P. of 1 pen = $ 50
    ∴ C.P. of 50 pens = 50 × 50 = $ 2500
    For profit of 10% ,

    S.P. =
    2500 × 110
    = $ 2750
    100

    S.P. of 40 pens at a loss of 5% =
    40 × 50 × 95
    = $ 1900
    100

    ∴ S.P. of remaining 10 pens = 2750 – 1900 = $ 850

    Correct Option: D

    Here , C.P. of 1 pen = $ 50
    ∴ C.P. of 50 pens = 50 × 50 = $ 2500
    For profit of 10% ,

    S.P. =
    2500 × 110
    = $ 2750
    100

    S.P. of 40 pens at a loss of 5% =
    40 × 50 × 95
    = $ 1900
    100

    ∴ S.P. of remaining 10 pens = 2750 – 1900 = $ 850
    Gain = S.P. of remaining 10 pens - C.P. of remaining 10 pens = 850 - 500 = $ 350
    ∴ Gain % =
    350
    × 100 = 70 %
    500