Percentage


  1. In an examination, a student who gets 20% of the maximum marks fails by 5 marks. Another student who scores 30% of the maximum marks gets 20 marks more than the pass marks. The necessary percentage required for passing is :









  1. View Hint View Answer Discuss in Forum

    Let the maximum marks be x.
    According to question,
    20% of x + 5 = 30% of x –20
    ⇒ (30 –20)% of x = 25

    ⇒ x =
    25 × 100
    = 250
    10

    ∴ Passing marks
    = 20% of 250 + 5 = 55
    ∴ % Passing marks
    =
    55
    × 100 = 22%
    250

    Aliter : Using Rule 22,
    Here, m = 30%, n = 20%, p = 5 and q = 20
    ∴ Maximum marks
    =
    100
    × (p + q)
    (n - m)

    =
    100
    × (5 + 20)
    (30 - 20)

    =
    100 × 25
    = 250
    10

    Passing marks
    = 20% of 250 + 5 = 55
    ∴ % of passing marks
    =
    55
    × 100 = 22%
    250

    Correct Option: C

    Let the maximum marks be x.
    According to question,
    20% of x + 5 = 30% of x –20
    ⇒ (30 –20)% of x = 25

    ⇒ x =
    25 × 100
    = 250
    10

    ∴ Passing marks
    = 20% of 250 + 5 = 55
    ∴ % Passing marks
    =
    55
    × 100 = 22%
    250

    Aliter : Using Rule 22,
    Here, m = 30%, n = 20%, p = 5 and q = 20
    ∴ Maximum marks
    =
    100
    × (p + q)
    (n - m)

    =
    100
    × (5 + 20)
    (30 - 20)

    =
    100 × 25
    = 250
    10

    Passing marks
    = 20% of 250 + 5 = 55
    ∴ % of passing marks
    =
    55
    × 100 = 22%
    250


  1. In an examination, there were 1000 boys and 800 girls. 60% of the boys and 50% of the girls passed. Find the percent of the candidates failed ?









  1. View Hint View Answer Discuss in Forum

    Total candidates
    = 1000 + 800 = 1800
    The candidates who are passed

    = 100 ×
    60
    + 800 ×
    50
    %
    100100

    = 600 + 400 = 1000
    The number of candidates who failed = 1800 – 1000 = 800
    ∴ Required percent
    =
    800
    × 100 = 44.4%
    1800

    Aliter : Using Rule 25,
    Percentage of passed students
    =
    B.b + G.g
    %
    B + G

    =
    1000 × 60 + 800 × 50
    1000 + 800

    =
    60000 + 40000
    1800

    =
    100000
    1800

    =
    500
    = 55.5
    9

    ∴ Percentage of failed students
    = 100 – 55.5 = 44.4%

    Correct Option: C

    Total candidates
    = 1000 + 800 = 1800
    The candidates who are passed

    = 100 ×
    60
    + 800 ×
    50
    %
    100100

    = 600 + 400 = 1000
    The number of candidates who failed = 1800 – 1000 = 800
    ∴ Required percent
    =
    800
    × 100 = 44.4%
    1800

    Aliter : Using Rule 25,
    Percentage of passed students
    =
    B.b + G.g
    %
    B + G

    =
    1000 × 60 + 800 × 50
    1000 + 800

    =
    60000 + 40000
    1800

    =
    100000
    1800

    =
    500
    = 55.5
    9

    ∴ Percentage of failed students
    = 100 – 55.5 = 44.4%



  1. If the price of petrol be raised by 20%, then the percentage by which a car owner must reduce his consumption so as not to increase his expenditure on petrol is









  1. View Hint View Answer Discuss in Forum

    Using Rule 8,
    Percentage decrease in the consumption of petrol

    =
    20
    × 100%
    100 + 20

    =
    50
    = 16
    2
    %
    33

    Correct Option: B

    Using Rule 8,
    Percentage decrease in the consumption of petrol

    =
    20
    × 100%
    100 + 20

    =
    50
    = 16
    2
    %
    33


  1. The price of petrol is increased by 25%. By how much per cent a car owner should reduce his consumption of petrol so that the expenditure on petrol would not be increased ?









  1. View Hint View Answer Discuss in Forum

    Using Rule 8,
    Required percent

    =
    25 × 100
    = 20%
    125

    Correct Option: D

    Using Rule 8,
    Required percent

    =
    25 × 100
    = 20%
    125



  1. Price of a commodity has increased by 60%. By what percent must a consumer reduce the consumption of the commodity so as not to increase the expenditure ?









  1. View Hint View Answer Discuss in Forum

    If the reduction in consumption be x%, then

    60 - x -
    60x
    = 0
    100

    ⇒ 60 - x -
    3x
    = 0
    5

    ⇒ 300 - 5x - 3x = 0
    ⇒ 8x = 300
    ⇒ x =
    300
    = 37.5%
    8

    Aliter : Using Rule 8,
    Required percentage
    =
    60
    × 100%
    160

    =
    300
    =
    75
    = 37.5%
    82

    Correct Option: B

    If the reduction in consumption be x%, then

    60 - x -
    60x
    = 0
    100

    ⇒ 60 - x -
    3x
    = 0
    5

    ⇒ 300 - 5x - 3x = 0
    ⇒ 8x = 300
    ⇒ x =
    300
    = 37.5%
    8

    Aliter : Using Rule 8,
    Required percentage
    =
    60
    × 100%
    160

    =
    300
    =
    75
    = 37.5%
    82