Percentage


  1. The price of an article was increased by r%. Later the new price was decreased by r%. If the latest price was 1, then the original price was :









  1. View Hint View Answer Discuss in Forum

    Let the initial value be A.
    When it is increased by r% it becomes :

    A + r% of A =
    A (r + 100)
    100

    Now, when it is decreased by r%, it becomes
    A (r + 100)
    – % of
    100

    A (r + 100)
    100

    =
    A(r + 100)
    1 -
    r
    100100

    =
    A(r + 100)(r - 100)
    10000

    ∴ A
    10000 - r2
    = 1
    10000

    ⇒ A = ₹
    10000
    10000 - r2

    Correct Option: D

    Let the initial value be A.
    When it is increased by r% it becomes :

    A + r% of A =
    A (r + 100)
    100

    Now, when it is decreased by r%, it becomes
    A (r + 100)
    – % of
    100

    A (r + 100)
    100

    =
    A(r + 100)
    1 -
    r
    100100

    =
    A(r + 100)(r - 100)
    10000

    ∴ A
    10000 - r2
    = 1
    10000

    ⇒ A = ₹
    10000
    10000 - r2


  1. A batsman scored 110 runs which included 3 boundaries and 8 sixes. What per cent of his total score, did he make by running between the wickets ?









  1. View Hint View Answer Discuss in Forum

    The batsman scored 3 × 4 + 8 × 6 = 60 runs by boundaries and sixes respectively. Then,
    Runs scored by running
    = 110 – 60 = 50
    ∴ Required percentage

    =
    50
    × 100 =
    500
    = 45
    5
    %
    1101111

    Correct Option: B

    The batsman scored 3 × 4 + 8 × 6 = 60 runs by boundaries and sixes respectively. Then,
    Runs scored by running
    = 110 – 60 = 50
    ∴ Required percentage

    =
    50
    × 100 =
    500
    = 45
    5
    %
    1101111



  1. Two numbers are more than the third number by 20% and 50% respectively. First number is what per cent of the second number ?









  1. View Hint View Answer Discuss in Forum

    Let third number = 100
    First number = 120
    Second number = 150
    Required percentage

    =
    120
    × 100 = 80%
    150

    Aliter : Using Rule 30,
    Required percentage
    =
    100 + 20
    × 100%
    100 + 50

    =
    120
    × 100%
    150

    =
    4
    × 100% = 80%
    5

    Correct Option: C

    Let third number = 100
    First number = 120
    Second number = 150
    Required percentage

    =
    120
    × 100 = 80%
    150

    Aliter : Using Rule 30,
    Required percentage
    =
    100 + 20
    × 100%
    100 + 50

    =
    120
    × 100%
    150

    =
    4
    × 100% = 80%
    5


  1. A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had :









  1. View Hint View Answer Discuss in Forum

    Let the fruit seller had originally x apples.
    According to the question;
    x – 40% of x = 420

    ⇒ x -
    40
    × x = 420
    100

    ⇒ x -
    2x
    = 420
    5

    5x - 2x
    = 420
    5

    3x
    = 420
    5

    ∴ x =
    420 × 5
    = 700
    3

    Method–2 :
    60% = 420 (Directly)
    ∴ 100% = 420 ×
    100
    = 700
    60

    Correct Option: D

    Let the fruit seller had originally x apples.
    According to the question;
    x – 40% of x = 420

    ⇒ x -
    40
    × x = 420
    100

    ⇒ x -
    2x
    = 420
    5

    5x - 2x
    = 420
    5

    3x
    = 420
    5

    ∴ x =
    420 × 5
    = 700
    3

    Method–2 :
    60% = 420 (Directly)
    ∴ 100% = 420 ×
    100
    = 700
    60



  1. 31% of employees pay tax in the year 2008. Non-tax paying employees are 20,700. The total number of employees are :









  1. View Hint View Answer Discuss in Forum

    Let the total number of employees be x.

    ∴ x ×
    69
    = 20700
    100

    ⇒ x =
    20700 × 100
    = 30000
    69

    Correct Option: C

    Let the total number of employees be x.

    ∴ x ×
    69
    = 20700
    100

    ⇒ x =
    20700 × 100
    = 30000
    69