Percentage


  1. The price of rice has increased by 60%. In order to restore the original price, the new price must be reduced by









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    Required per cent

    =
    x
    × 100
    100 + x

    where x = 60%
    =
    60
    × 100 =
    75
    = 37
    1
    %
    16022

    Correct Option: B

    Required per cent

    =
    x
    × 100
    100 + x

    where x = 60%
    =
    60
    × 100 =
    75
    = 37
    1
    %
    16022


  1. The price of an item was increased by 10%. This reduced the monthly total sales by 20%. The overall effect on the value of monthly sales is a









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    Required percentage change

    = 10 - 20 +
    10 × (-20)
    %
    100

    = –12% Negative sign shows decrease.
    Aliter : Using Rule 4,
    Required percentage
    = 10 - 20 -
    10 × 20
    = (–10 – 2) = 12% decrease.
    100

    Correct Option: D

    Required percentage change

    = 10 - 20 +
    10 × (-20)
    %
    100

    = –12% Negative sign shows decrease.
    Aliter : Using Rule 4,
    Required percentage
    = 10 - 20 -
    10 × 20
    = (–10 – 2) = 12% decrease.
    100



  1. A reduction of 20% in the price of sugar enables a purchaser to obtain 8 kg more for Rs. 160. Then the price per kg before reduction was









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    Let the original price of sugar be Rs. x per kg.
    Reduced price

    = Rs
    80x
    = Rs.
    4x
    per kg.
    1005

    According to the question,
    160
    -
    160
    = 8
    4x
    x
    5

    40 × 5
    -
    160
    = 8
    xx

    200
    -
    160
    = 8
    xx

    40
    = 8
    x

    ⇒ 8x = 40
    ⇒ x =
    40
    = 5 per kg
    8

    Reduced Price
    =
    4x
    =
    4 × 5
    = Rs. 4 per kg
    55

    Aliter : Using Rule 31,
    Reduced price per kg.
    =
    21 × 160
    = Rs. 4
    100 × 8

    Correct Option: A

    Let the original price of sugar be Rs. x per kg.
    Reduced price

    = Rs
    80x
    = Rs.
    4x
    per kg.
    1005

    According to the question,
    160
    -
    160
    = 8
    4x
    x
    5

    40 × 5
    -
    160
    = 8
    xx

    200
    -
    160
    = 8
    xx

    40
    = 8
    x

    ⇒ 8x = 40
    ⇒ x =
    40
    = 5 per kg
    8

    Reduced Price
    =
    4x
    =
    4 × 5
    = Rs. 4 per kg
    55

    Aliter : Using Rule 31,
    Reduced price per kg.
    =
    21 × 160
    = Rs. 4
    100 × 8


  1. A reduction of 21% in the price of an item enables a person to buy 3 kg more for ₹ 100. The reduced price of item per kg is









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    Original price of article = ₹ x per kg.

    New price = ₹
    79x
    per kg
    100

    100
    -
    100
    = 3
    79x
    x
    100

    10000
    -
    100
    = 3
    79xx

    10000 - 7900
    = 3
    79x

    2100
    = 3
    79x

    700
    = 1
    79x

    ⇒ 79x = 700
    ⇒ x =
    700
    79

    ∴ New price =
    79x
    =
    79
    ×
    700
    = ₹ 7 per kg
    10010079

    Aliter : Using Rule 31,
    Reduced price per kg.
    =
    21 × 100
    = ₹ 7
    100 × 3

    Correct Option: D

    Original price of article = ₹ x per kg.

    New price = ₹
    79x
    per kg
    100

    100
    -
    100
    = 3
    79x
    x
    100

    10000
    -
    100
    = 3
    79xx

    10000 - 7900
    = 3
    79x

    2100
    = 3
    79x

    700
    = 1
    79x

    ⇒ 79x = 700
    ⇒ x =
    700
    79

    ∴ New price =
    79x
    =
    79
    ×
    700
    = ₹ 7 per kg
    10010079

    Aliter : Using Rule 31,
    Reduced price per kg.
    =
    21 × 100
    = ₹ 7
    100 × 3



  1. A number, on subtracting 15 from it, reduces to its 80%. What is 40% of the number?









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    If the number be ₹ x, then

    x – 15 =
    4x
    5

    ⇒ 5x – 75 = 4x ⇒ x = 75
    ∴ 40% of 75 =
    75 × 40
    = 30
    100

    Correct Option: C

    If the number be ₹ x, then

    x – 15 =
    4x
    5

    ⇒ 5x – 75 = 4x ⇒ x = 75
    ∴ 40% of 75 =
    75 × 40
    = 30
    100