Time and Work


  1. A and B can do a piece of work in 10 days. B and C can do it in 12 days. A and C can do it in 15 days. How long will A take to do it alone ?









  1. View Hint View Answer Discuss in Forum

    (A+B)’s 1 day’s work =
    1
    10

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

    (C + A)’s 1 day’s work =
    1
    15

    On adding all three,
    2(A + B + C)’s 1 day’s work =
    1
    +
    1
    +
    1
    101215

    2(A + B + C)’s 1 day’s work =
    6 + 5 + 4
    60

    2(A + B + C)’s 1 day’s work =
    15
    =
    1
    604

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

    ∴ A’s 1 day’s work =
    1
    -
    1
    812

    A’s 1 day’s work =
    3 - 2
    =
    1
    2424

    ∴ A will complete the work in 24 days.
    Second method to solve this question ,
    Here , x = 10 , y = 12 , z = 15
    A alone can do in =
    2 × x × y × z
    xy + yz + zx

    Correct Option: A

    (A+B)’s 1 day’s work =
    1
    10

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

    (C + A)’s 1 day’s work =
    1
    15

    On adding all three,
    2(A + B + C)’s 1 day’s work =
    1
    +
    1
    +
    1
    101215

    2(A + B + C)’s 1 day’s work =
    6 + 5 + 4
    60

    2(A + B + C)’s 1 day’s work =
    15
    =
    1
    604

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

    ∴ A’s 1 day’s work =
    1
    -
    1
    812

    A’s 1 day’s work =
    3 - 2
    =
    1
    2424

    ∴ A will complete the work in 24 days.
    Second method to solve this question ,
    Here , x = 10 , y = 12 , z = 15
    A alone can do in =
    2 × x × y × z
    xy + yz + zx

    A alone can do in =
    2 × 10 × 12 × 15
    10 × 12 + 12 × 15 - 15 × 10

    A alone can do in =
    3600
    120 + 180 - 150

    A alone can do in =
    3600
    = 24 days
    150


  1. A and B can do a piece of work in 8 days, B and C can do it in 24 days, while C and A
    can do it in 8
    7
    days. In how many days can C do it alone?
    4










  1. View Hint View Answer Discuss in Forum

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

    (B + C)’s 1 day’s work =
    1
    24

    (C + A)’s 1 day’s work =
    7
    60

    On adding all three,
    2 (A + B + C)’s 1 day’s work =
    1
    +
    1
    +
    7
    82460

    2 (A + B + C)’s 1 day’s work =
    15 + 5 + 14
    =
    34
    120120

    ∴ (A + B + C)’s 1 day’s work =
    17
    120

    ∴ C’s 1 day’s work =
    17
    -
    1
    1208

    C’s 1 day’s work =
    17 - 15
    =
    1
    12060

    ∴ C alone will complete the work in 60 days.
    Second method to solve this question ,
    Here , x = 8 , y = 24 , z = 60/7
    C alone can do in =
    2xyz
    xy - yz + zx

    Correct Option: A

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

    (B + C)’s 1 day’s work =
    1
    24

    (C + A)’s 1 day’s work =
    7
    60

    On adding all three,
    2 (A + B + C)’s 1 day’s work =
    1
    +
    1
    +
    7
    82460

    2 (A + B + C)’s 1 day’s work =
    15 + 5 + 14
    =
    34
    120120

    ∴ (A + B + C)’s 1 day’s work =
    17
    120

    ∴ C’s 1 day’s work =
    17
    -
    1
    1208

    C’s 1 day’s work =
    17 - 15
    =
    1
    12060

    ∴ C alone will complete the work in 60 days.
    Second method to solve this question ,
    Here , x = 8 , y = 24 , z = 60/7
    C alone can do in =
    2xyz
    xy - yz + zx

    C alone can do in = 2 × 8 × 24 ×
    60
    7
    8 × 24 - 24 ×
    60
    +
    60
    × 8
    77

    C alone can do in =
    23040
    7
    192 -
    1440
    +
    480
    77

    C alone can do in =
    23040
    7
    1344 - 1440 + 480
    7

    C alone can do in =
    23040
    ×
    7
    = 60 days
    7384



  1. A, B and C together can complete a piece of work in 30 minutes. A and B together can complete the same work in 50 minutes. C alone can complete the work in









  1. View Hint View Answer Discuss in Forum

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

    Work done by (A + B) in 1 minute =
    1
    50

    ∴ Work done by C alone in 1 minute =
    1
    -
    1
    3050

    Work done by C alone in 1 minute =
    5 - 3
    150

    Work done by C alone in 1 minute =
    2
    =
    1
    15075

    ∴ C alone will complete the work in 75 minutes.
    Second method to solve this question ,
    Here , x = 50 , y = 30

    Correct Option: B

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

    Work done by (A + B) in 1 minute =
    1
    50

    ∴ Work done by C alone in 1 minute =
    1
    -
    1
    3050

    Work done by C alone in 1 minute =
    5 - 3
    150

    Work done by C alone in 1 minute =
    2
    =
    1
    15075

    ∴ C alone will complete the work in 75 minutes.
    Second method to solve this question ,
    Here , x = 50 , y = 30
    C alone can do in =
    xy
    x - y

    C alone can do in =
    50 × 30
    = 75 minutes
    50 - 30


  1. A and B together can do a piece of work in 5 days and A alone can do it in 8 days. B alone can do the same piece of work in









  1. View Hint View Answer Discuss in Forum

    (A + B)’s 1 day’s work =
    1
    5

    A’s 1 day’s work =
    1
    8

    ∴ B’s 1 day’s work =
    1
    -
    1
    58

    B’s 1 day’s work =
    8 - 5
    =
    3
    4040

    ∴ B alone will complete the work in
    40
    = 13
    1
    days
    33

    Second method to solve this question ,
    Here , x = 5 , y = 8

    Correct Option: C

    (A + B)’s 1 day’s work =
    1
    5

    A’s 1 day’s work =
    1
    8

    ∴ B’s 1 day’s work =
    1
    -
    1
    58

    B’s 1 day’s work =
    8 - 5
    =
    3
    4040

    ∴ B alone will complete the work in
    40
    = 13
    1
    days
    33

    Second method to solve this question ,
    Here , x = 5 , y = 8
    Time taken by B =
    5 × 8
    8 - 5

    Time taken by B =
    40
    = 13
    1
    days
    33



  1. A and B together can complete a piece of work in 18 days, B and C in 24 days and A and C in 36 days. In how many days, will all of them together complete the work ?









  1. View Hint View Answer Discuss in Forum

    (A + B)’s 1 day’s work =
    1
    18

    (B + C)’s 1 day’s work =
    1
    24

    (A + C)’s 1 day’s work =
    1
    36

    Adding all three,
    2 (A + B + C)’s 1 day’s work =
    1
    +
    1
    +
    1
    182436

    2 (A + B + C)’s 1 day’s work =
    4 + 3 + 2
    =
    1
    728

    ∴ (A + B + C)’ 1 day’s work =
    1
    16

    ∴ A, B and C together will complete the work in 16 days.
    Second method to solve this question ,
    Here , x = 18 , y = 24 , z = 36
    Time taken =
    2xyz
    xy + yz + zx

    Correct Option: A

    (A + B)’s 1 day’s work =
    1
    18

    (B + C)’s 1 day’s work =
    1
    24

    (A + C)’s 1 day’s work =
    1
    36

    Adding all three,
    2 (A + B + C)’s 1 day’s work =
    1
    +
    1
    +
    1
    182436

    2 (A + B + C)’s 1 day’s work =
    4 + 3 + 2
    =
    1
    728

    ∴ (A + B + C)’ 1 day’s work =
    1
    16

    ∴ A, B and C together will complete the work in 16 days.
    Second method to solve this question ,
    Here , x = 18 , y = 24 , z = 36
    Time taken =
    2xyz
    xy + yz + zx

    Total time taken =
    2 × 18 × 24 × 36
    18 × 24 + 24 × 36 + 36 × 18

    Total time taken =
    36 × 24 × 36
    432 + 864 + 648

    Total time taken =
    31104
    = 16 days
    1944