Time and Work


  1. A and B together can complete a work in 8 days and B and C to- gether in 12 days. All of the three together can complete the work in 6 days. In how much time will A and C together complete the work ?









  1. View Hint View Answer Discuss in Forum

    Let A and C complete the work in y days

    (A + B)’s 1 day’s work =
    1
    8

    (B + C)’s 1 day’s work =
    1
    12

    (C + A)’s 1 day’s work =
    1
    y

    Then (A + B + B + C + C + A)’s 1 day’s work =
    1
    +
    1
    +
    1
    812y

    2(A + B + C)’s 1 day’s work =
    3y + 2y + 24
    24y

    (A + B + C)’s 1 day’s work =
    5y + 24
    24y × 2

    According to the question,
    (A + B + C)’s 1 day’s work =
    1
    6

    1
    =
    5y + 24
    648y

    ⇒ 30y + 144 = 48y
    ∴ =
    144
    = 8 days
    18

    Second method to solve this question ,
    Here , p = 8 , q = 12 , r = y
    Time taken =
    2pqr
    pq + qr + rp

    Correct Option: A

    Let A and C complete the work in y days

    (A + B)’s 1 day’s work =
    1
    8

    (B + C)’s 1 day’s work =
    1
    12

    (C + A)’s 1 day’s work =
    1
    y

    Then (A + B + B + C + C + A)’s 1 day’s work =
    1
    +
    1
    +
    1
    812y

    2(A + B + C)’s 1 day’s work =
    3y + 2y + 24
    24y

    (A + B + C)’s 1 day’s work =
    5y + 24
    24y × 2

    According to the question,
    (A + B + C)’s 1 day’s work =
    1
    6

    1
    =
    5y + 24
    648y

    ⇒ 30y + 144 = 48y
    ∴ =
    144
    = 8 days
    18

    Second method to solve this question ,
    Let the time taken by A and C be y days
    Here , p = 8 , q = 12 , r = y
    Time taken =
    2pqr
    pq + qr + rp

    ⇒ Total time taken =
    2 × 8 × 12 × y
    8 × 12 + 12 × y + 8 × y

    6 =
    192y
    96 + 20y

    ⇒ 576 + 120y = 192y
    ⇒ 72y = 576
    ⇒ y = 8
    Time taken by A and C is 8 days.


  1. A and B can complete a piece of work in 30 days, B and C in 20 days, while C and A in 15 days. If all of them work together, the time taken in completing the work will be









  1. View Hint View Answer Discuss in Forum

    Work done by (A + B) in 1 day =
    1
    30

    Work done by (B + C) in 1 day =
    1
    20

    Work done by (C + A) in 1 day =
    1
    15

    On adding,
    Work done by 2 (A +B + C) in 1 day =
    1
    +
    1
    +
    1
    302015

    Work done by 2 (A +B + C) in 1 day =
    2 + 3 + 4
    60

    Work done by 2 (A +B + C) in 1 day =
    9
    =
    3
    6020

    ∴ Work done by (A + B + C) in 1day =
    3
    40

    ∴ (A + B + C) will do the work in
    40
    = 13
    1
    days
    33

    Second method to solve this question ,
    Here , x = 30 , y = 20 , z = 15

    Correct Option: D

    Work done by (A + B) in 1 day =
    1
    30

    Work done by (B + C) in 1 day =
    1
    20

    Work done by (C + A) in 1 day =
    1
    15

    On adding,
    Work done by 2 (A +B + C) in 1 day =
    1
    +
    1
    +
    1
    302015

    Work done by 2 (A +B + C) in 1 day =
    2 + 3 + 4
    60

    Work done by 2 (A +B + C) in 1 day =
    9
    =
    3
    6020

    ∴ Work done by (A + B + C) in 1day =
    3
    40

    ∴ (A + B + C) will do the work in
    40
    = 13
    1
    days
    33

    Second method to solve this question ,
    Here , x = 30 , y = 20 , z = 15
    Time taken =
    2xyz
    xy + yz + zx

    Time taken =
    2 × 30 × 20 × 15
    30 × 20 + 20 × 15 + 15 × 30

    Time taken =
    18000
    600 + 300 + 450

    Time taken =
    18000
    = 13
    1
    days
    13503



  1. A and B can do a piece of work in 12 days, B and C in 8 days and C and A in 6 days. How long would B take to do the same work alone ?









  1. View Hint View Answer Discuss in Forum

    (A + B)'s 1 day's work =
    1
    .....(i)
    12

    (B + C)'s 1 day's work =
    1
    .....(ii)
    8

    (C + A)'s 1 day's work =
    1
    .....(iii)
    6

    On adding,
    2(A + B + C)'s 1 day's work =
    1
    +
    1
    +
    1
    1286

    2(A + B + C)'s 1 day's work =
    2 + 3 + 4
    =
    9
    2424

    ∴ (A+ B + C)'s 1 day’s work =
    9
    =
    9
    .....(iv)
    24 × 248

    On, subtracting (iii) from (iv),
    B’s 1 day’s work =
    9
    -
    1
    486

    B’s 1 day’s work =
    9 - 8
    =
    1
    4848

    ∴ B can complete the work in 48 days.
    Second method to solve this question ,
    Here , x = 12 , y = 8 , z = 6
    Time taken =
    2xyz
    - xy + yz + zx

    Correct Option: D

    (A + B)'s 1 day's work =
    1
    .....(i)
    12

    (B + C)'s 1 day's work =
    1
    .....(ii)
    8

    (C + A)'s 1 day's work =
    1
    .....(iii)
    6

    On adding,
    2(A + B + C)'s 1 day's work =
    1
    +
    1
    +
    1
    1286

    2(A + B + C)'s 1 day's work =
    2 + 3 + 4
    =
    9
    2424

    ∴ (A+ B + C)'s 1 day’s work =
    9
    =
    9
    .....(iv)
    24 × 248

    On, subtracting (iii) from (iv),
    B’s 1 day’s work =
    9
    -
    1
    486

    B’s 1 day’s work =
    9 - 8
    =
    1
    4848

    ∴ B can complete the work in 48 days.
    Second method to solve this question ,
    Here , x = 12 , y = 8 , z = 6
    Time taken =
    2xyz
    - xy + yz + zx

    B alone can do in =
    2 × 12 × 8 × 6
    - 12 × 8 + 8 × 6 + 6 × 12

    Time taken =
    24 × 48
    - 96 + 48 + 72

    Time taken =
    24 × 48
    - 96 + 120

    Time taken =
    24 × 48
    = 48 days.
    24


  1. A and B together can do a work in 8 days, B and C together in 6 days while C and A together in 10 days, if they all work together, the work will be completed in :









  1. View Hint View Answer Discuss in Forum

    (A + B)'s 1 day's work =
    1
    .....(i)
    8

    (B + C)'s 1 day's work =
    1
    .....(ii)
    6

    (C + A)'s 1 day's work =
    1
    .....(iii)
    10

    On adding all three equations ,
    2(A + B + C)'s 1 day's work =
    1
    +
    1
    +
    1
    8610

    2(A + B + C)'s 1 day's work =
    15 + 20 + 12
    =
    47
    120120

    ⇒ (A + B + C)'s 1 day’s work =
    47
    240

    Correct Option: C

    (A + B)'s 1 day's work =
    1
    .....(i)
    8

    (B + C)'s 1 day's work =
    1
    .....(ii)
    6

    (C + A)'s 1 day's work =
    1
    .....(iii)
    10

    On adding all three equations ,
    2(A + B + C)'s 1 day's work =
    1
    +
    1
    +
    1
    8610

    2(A + B + C)'s 1 day's work =
    15 + 20 + 12
    =
    47
    120120

    ⇒ (A + B + C)'s 1 day’s work =
    47
    240

    ∴ (A + B + C) together will complete the work in
    240
    = 5
    5
    days.
    4747

    Second method to solve this question ,
    Here , x = 8 , y = 6 , z = 10
    Time taken =
    2xyz
    xy + yz + zx

    Time taken =
    2 × 8 × 6 × 10
    8 × 6 + 6 × 10 + 10 × 8

    Time taken =
    960
    48 + 60 + 80

    Time taken =
    960
    188

    Time taken =
    240
    = 5
    5
    days.
    4747



  1. A and B together can complete a piece of work in 72 days, B and C together can complete it in 120 days, and A and C together in 90 days. In what time can A alone complete the work ?









  1. View Hint View Answer Discuss in Forum

    (A + B)’s 1 day’s work =
    1
    72

    (B + C)’s 1 day’s work =
    1
    120

    (C + A)’s 1 day’s work =
    1
    90

    Adding all three,
    2(A + B + C)’s 1 day’s work =
    1
    +
    1
    +
    1
    7212090

    2(A + B + C)’s 1 day’s work =
    5 + 3 + 4
    =
    12
    =
    1
    36036030

    ∴ (A + B + C)’s 1 day’s work =
    1
    60

    Now, A’s 1 day’s work = (A + B + C)’s 1 day’s work - (B + C)’s 1 day’s work
    A’s 1 day’s work =
    1
    -
    1
    60120

    A’s 1 day’s work =
    2 - 1
    =
    1
    120120

    ∴ A alone can complete the work in 120 days.
    Second method to solve this question ,
    Here , x = 72 , y = 120 , z = 90
    A alone can do in =
    2xyz
    xy + yz - zx

    Correct Option: C

    (A + B)’s 1 day’s work =
    1
    72

    (B + C)’s 1 day’s work =
    1
    120

    (C + A)’s 1 day’s work =
    1
    90

    Adding all three,
    2(A + B + C)’s 1 day’s work =
    1
    +
    1
    +
    1
    7212090

    2(A + B + C)’s 1 day’s work =
    5 + 3 + 4
    =
    12
    =
    1
    36036030

    ∴ (A + B + C)’s 1 day’s work =
    1
    60

    Now, A’s 1 day’s work = (A + B + C)’s 1 day’s work - (B + C)’s 1 day’s work
    A’s 1 day’s work =
    1
    -
    1
    60120

    A’s 1 day’s work =
    2 - 1
    =
    1
    120120

    ∴ A alone can complete the work in 120 days.
    Second method to solve this question ,
    Here , x = 72 , y = 120 , z = 90
    A alone can do in =
    2xyz
    xy + yz - zx

    A alone can do in =
    2 × 72 × 120 × 90
    72 × 120 + 120 × 90 - 72 × 90

    A alone can do in =
    2 × 72 × 120 × 90
    8640 + 10800 – 6480

    A alone can do in =
    144 × 10800
    = 120 days
    12960