Time and Work


  1. A and B together can complete a work in 15 days. A is 50% more efficient worker than B. How long will A take to complete the work alone ?











  1. View Hint View Answer Discuss in Forum

    Ratio of the work of A and B
    done in 1 day = 3 : 2
    [∵ B's work doen = x (let), then

    A's work done =
    x + 50
    x =
    3
    x
    1002

    So, (A : B)'s work done =
    3
    x : x or 3 : 2]
    2

    ∵ Work done by A and B together in 1 day
    =
    1
    15

    ∴ A’s 1 day’s work =
    1
    ×
    3
    155

    =
    1
    25

    Hence, A alone will finish the work in 25 days.
    Aliter : Using Rule 22,
    Here, n =
    3
    2

    because A is 50% more efficient than B.
    D = 15
    Time taken by A
    =
    n + 1
    × D
    n

    =
    (3/2) + 1
    × 15 = 25 days
    3/2

    Correct Option: E

    Ratio of the work of A and B
    done in 1 day = 3 : 2
    [∵ B's work doen = x (let), then

    A's work done =
    x + 50
    x =
    3
    x
    1002

    So, (A : B)'s work done =
    3
    x : x or 3 : 2]
    2

    ∵ Work done by A and B together in 1 day
    =
    1
    15

    ∴ A’s 1 day’s work =
    1
    ×
    3
    155

    =
    1
    25

    Hence, A alone will finish the work in 25 days.
    Aliter : Using Rule 22,
    Here, n =
    3
    2

    because A is 50% more efficient than B.
    D = 15
    Time taken by A
    =
    n + 1
    × D
    n

    =
    (3/2) + 1
    × 15 = 25 days
    3/2


  1. A is twice as good a workman as B and B is twice as good a workman as C. If A and B can together finish a piece of work in 4 days, then C can do it by himself in









  1. View Hint View Answer Discuss in Forum

    Using basics of Rule 2,
    According to the question,
    If A takes x days to complete the work, B will take 2x days and C will take 4x days,
    Now, (A + B)'s 1 day’s work

    =
    1
    4

    =
    1
    +
    2
    =
    1
    x2x4

    2 + 1
    =
    1
    2x4

    ⇒ 2x = 12 ⇒ x = 6
    ∴ C will complete the work in 4x
    i.e. 24 days.

    Correct Option: C

    Using basics of Rule 2,
    According to the question,
    If A takes x days to complete the work, B will take 2x days and C will take 4x days,
    Now, (A + B)'s 1 day’s work

    =
    1
    4

    =
    1
    +
    2
    =
    1
    x2x4

    2 + 1
    =
    1
    2x4

    ⇒ 2x = 12 ⇒ x = 6
    ∴ C will complete the work in 4x
    i.e. 24 days.



  1. To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it ?









  1. View Hint View Answer Discuss in Forum

    Using basics of Rule 2,
    Let B alone can do the work in x days

    ∴ A can do the work in
    3x
    days.
    2

    According to the question,
    =
    1
    +
    2
    =
    1
    x3x18

    3 + 2
    =
    1
    3x18

    5
    =
    1
    3x18

    ⇒ 3x = 18 × 5
    ⇒ x =
    18 × 5
    = 30 days
    3

    Correct Option: A

    Using basics of Rule 2,
    Let B alone can do the work in x days

    ∴ A can do the work in
    3x
    days.
    2

    According to the question,
    =
    1
    +
    2
    =
    1
    x3x18

    3 + 2
    =
    1
    3x18

    5
    =
    1
    3x18

    ⇒ 3x = 18 × 5
    ⇒ x =
    18 × 5
    = 30 days
    3


  1. A 10 hectare field is reaped by 2 men, 3 women and 4 children together in 10 days. If working capabilities of a man, a woman and a child are in the ratio 5 : 4 : 2, then a 16 hectare field will be reaped by 6 men,4 women and 7 children in









  1. View Hint View Answer Discuss in Forum

    Using Rule 1,
    Ratio of the working capabilities of a man, a woman and a child = 5 : 4 : 2
    ∴ Ratio of man, woman and child equivalence

    =
    1
    :
    1
    :
    1
    542

    =
    1
    × 20 :
    1
    × 20 :
    1
    × 20
    542

    = 4 : 5 : 10
    or 4 men ≡ 5 women ≡ 10 children 4 men = 10 children
    ∴ 2 men ≡ 5 children and 6 men ≡ 15 children
    5 women = 10 children
    ∴ 3 women ≡ 6 children
    4 women ≡ 8 children
    ∴ 2 men + 3 women + 4 Children = 15 children
    6 men + 4 women + 7 children = 30 children

    where, x is no. of days
    ⇒ 30 × 10 × x = 15 × 16 × 10
    ⇒ x =
    15 × 16 × 10
    = 8 days
    30 × 10

    Correct Option: D

    Using Rule 1,
    Ratio of the working capabilities of a man, a woman and a child = 5 : 4 : 2
    ∴ Ratio of man, woman and child equivalence

    =
    1
    :
    1
    :
    1
    542

    =
    1
    × 20 :
    1
    × 20 :
    1
    × 20
    542

    = 4 : 5 : 10
    or 4 men ≡ 5 women ≡ 10 children 4 men = 10 children
    ∴ 2 men ≡ 5 children and 6 men ≡ 15 children
    5 women = 10 children
    ∴ 3 women ≡ 6 children
    4 women ≡ 8 children
    ∴ 2 men + 3 women + 4 Children = 15 children
    6 men + 4 women + 7 children = 30 children

    where, x is no. of days
    ⇒ 30 × 10 × x = 15 × 16 × 10
    ⇒ x =
    15 × 16 × 10
    = 8 days
    30 × 10



  1. A can do a piece of work in 70 days and B is 40% more efficient than A. The number of days taken by B to do the same work is









  1. View Hint View Answer Discuss in Forum

    A : B = D2 : D2
    ⇒ 100 : 140 = D2 : 70
    ⇒ 100 × 70 = 140 × D2

    ⇒ D2 =
    100 × 70
    = 50 days.
    140

    Aliter : Using Rule 17,
    Here, x = 70, r = 40%
    Time taken by B
    = x ×
    100
    100 + R

    =
    70 × 100
    = 50 days
    100 + 40

    Correct Option: C

    A : B = D2 : D2
    ⇒ 100 : 140 = D2 : 70
    ⇒ 100 × 70 = 140 × D2

    ⇒ D2 =
    100 × 70
    = 50 days.
    140

    Aliter : Using Rule 17,
    Here, x = 70, r = 40%
    Time taken by B
    = x ×
    100
    100 + R

    =
    70 × 100
    = 50 days
    100 + 40