Percentage


  1. The ratio of two numbers is 4 : 5 when the first is increased by 20% and the second is decreased by 20%, the ratio of the resulting numbers is









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    Let the numbers be 4k and m5k .
    After corresponding increase or decrease,

    Required ratio = 4k ×
    120
    : 5k ×
    80
    100100

    Correct Option: D

    Let the numbers be 4k and m5k .
    After corresponding increase or decrease,

    Required ratio = 4k ×
    120
    : 5k ×
    80
    100100

    Hence , Required ratio = 12k : 10k = 6 : 5


  1. Rama’s expenditures and savings are in the ratio 5 : 3. If her in- come increases by 12% and expenditure by 15%, then by how much per cent do her savings increase ?









  1. View Hint View Answer Discuss in Forum

    Let Rama’s expenditure = 5k
    Savings = 3k
    ∴ Rama’s income = 5k + 3k = 8k
    After increase,

    Rama’s income =
    112
    × 8k = 8.96 k
    100

    Rama’s expenditure =
    5k × 115
    = 5.75k
    100

    Rama’s savings = (8.96k – 5.75k) = 3.21k

    Correct Option: B

    Let Rama’s expenditure = 5k
    Savings = 3k
    ∴ Rama’s income = 5k + 3k = 8k
    After increase,

    Rama’s income =
    112
    × 8k = 8.96 k
    100

    Rama’s expenditure =
    5k × 115
    = 5.75k
    100

    Rama’s savings = (8.96k – 5.75k) = 3.21k
    ∴ Rama’s saving percent =
    3.21k - 3k
    × 100
    3k

    Rama’s saving percent =
    0.21
    × 100 = 7%
    3



  1. The price of sugar is increased by 20%. If the expenditure on sugar has to be kept the same as earlier, the ratio between the reduction in consumption and the original consumption is









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    The raised price =
    120
    of the former price
    100

    ∴ The householder must now consume
    100
    of the original amount
    120

    ∴ The reduction in consumption = 1 -
    100
    of the original consumption
    120

    =
    1
    of the original consumption
    6

    Required ratio = 1 : 6
    Second method to solve this question ,
    Required percentage =
    20
    × 100
    100 + 20

    Correct Option: C

    The raised price =
    120
    of the former price
    100

    ∴ The householder must now consume
    100
    of the original amount
    120

    ∴ The reduction in consumption = 1 -
    100
    of the original consumption
    120

    =
    1
    of the original consumption
    6

    Required ratio = 1 : 6
    Second method to solve this question ,
    Required percentage =
    20
    × 100
    100 + 20

    Required percentage =
    20
    × 100
    120

    Required percentage =
    100
    %
    6

    Required ratio = 1 : 6


  1. The difference of two numbers is 15% of their sum. The ratio of the larger number to the smaller number is









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    Let the numbers be p and q
    where p > q. Then,

    p - q =
    15
    (p + q)
    100

    ⇒ p - q =
    3
    (p + q)
    20

    ⇒ 20p – 20q = 3p + 3q
    ⇒ 20p – 3p = 20q + 3q

    Correct Option: A

    Let the numbers be p and q
    where p > q. Then,

    p - q =
    15
    (p + q)
    100

    ⇒ p - q =
    3
    (p + q)
    20

    ⇒ 20p – 20q = 3p + 3q
    ⇒ 20p – 3p = 20q + 3q
    ⇒ 17p = 23q ⇒
    p
    =
    23
    q17



  1. The bus fare and train fare of a place from Kolkata were 20 and 30 respectively. Train fare has been increased by 20% and the bus fare has been increased by 10%. The ratio of new train fare to new bus fare is









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    Increased train fare = ₹
    120
    × 30= ₹ 36
    100

    Correct Option: B

    Increased train fare = ₹
    120
    × 30= ₹ 36
    100

    Increased bus fare = ₹
    110
    × 20= ₹ 22
    100

    ∴ Required ratio = 36 : 22 = 18 : 11