Time and Work


  1. A can do 1/3 rd of a work in 5 days and B can do 2/5 th of this work in 10 days. Both A and B, together can do the work in









  1. View Hint View Answer Discuss in Forum

    ∵ A does 1/3 rd part of work in 5 days.
    ∴ A will do 1 work in 5 × 3 = 15 days.
    ∵ B does 2/5 th of work in 10 days

    ∴ B will do 1 work in
    10 × 5
    = 25 days.
    2

    ∴ (A + B)’s 1 day’s work
    =
    1
    +
    1
    1525

    =
    5 + 3
    =
    8
    7575

    ∴ Required time =
    75
    = 9
    3
    88

    Correct Option: C

    ∵ A does 1/3 rd part of work in 5 days.
    ∴ A will do 1 work in 5 × 3 = 15 days.
    ∵ B does 2/5 th of work in 10 days

    ∴ B will do 1 work in
    10 × 5
    = 25 days.
    2

    ∴ (A + B)’s 1 day’s work
    =
    1
    +
    1
    1525

    =
    5 + 3
    =
    8
    7575

    ∴ Required time =
    75
    = 9
    3
    88


  1. A and B together can complete a work in 24 days. B alone does 1/3 rd part of this work in 12 days. How many days will A alone take to complete the remaining work?









  1. View Hint View Answer Discuss in Forum

    ∵ B completes
    1
    work in 12 days.
    3

    ∴ B will complete 1 work in 12 × 3 = 36 days.
    ∴ B’s 1 day’s work =
    1
    36

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

    ∴ A’s 1 day’s work =
    1
    -
    1
    2436

    =
    3 - 2
    =
    1
    7272

    ∴ Time taken by A in doing 1 work = 72 days
    Remaining work = 1 –
    1
    =
    2
    33

    ∴ Time taken by A in doing
    2
    work =
    2
    × 72 = 48 days
    33

    Correct Option: C

    ∵ B completes
    1
    work in 12 days.
    3

    ∴ B will complete 1 work in 12 × 3 = 36 days.
    ∴ B’s 1 day’s work =
    1
    36

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

    ∴ A’s 1 day’s work =
    1
    -
    1
    2436

    =
    3 - 2
    =
    1
    7272

    ∴ Time taken by A in doing 1 work = 72 days
    Remaining work = 1 –
    1
    =
    2
    33

    ∴ Time taken by A in doing
    2
    work =
    2
    × 72 = 48 days
    33



  1. A can do a certain job in 12 days. B is 60% more efficient than A. Then B can do the same piece of work in









  1. View Hint View Answer Discuss in Forum

    A can do a work in 12 days.
    B is 60% more efficient than A.
    ∴ Time taken by B

    =
    100
    × 12days
    160

    =
    15
    = 7
    1
    22

    Correct Option: B

    A can do a work in 12 days.
    B is 60% more efficient than A.
    ∴ Time taken by B

    =
    100
    × 12days
    160

    =
    15
    = 7
    1
    22


  1. Dhiru can dig 1/a of a field in 20 hours. What fraction of the same field can Kaku dig in 20 hours if the two of them can dig the field in 60 hours, working together at their respective rates ?









  1. View Hint View Answer Discuss in Forum

    ∵ Dhiru digs
    1
    part of field in 20 hours.
    a

    ∴ Dhiru digs 1 part of field in 20a hours
    =
    1
    -
    1
    =
    a - 3
    6020a60a

    ∴ Part of field dug by Kaku in 1 hour
    =
    20(a - 3)
    =
    a - 3
    60a3a

    Correct Option: D

    ∵ Dhiru digs
    1
    part of field in 20 hours.
    a

    ∴ Dhiru digs 1 part of field in 20a hours
    =
    1
    -
    1
    =
    a - 3
    6020a60a

    ∴ Part of field dug by Kaku in 1 hour
    =
    20(a - 3)
    =
    a - 3
    60a3a



  1. A and B work together to complete the rest of a job in 7 days.However, 37/100 of the job was already done. Also, the work done by A in 5 days is equal to the work done by B in 4 days. How many days would be required by the fastest worker to complete the entire work?









  1. View Hint View Answer Discuss in Forum

    Remaining work

    = 1 –
    37
    100

    =
    100 - 37
    =
    63
    100100

    ∴ Time taken by (A + B) in doing
    63
    part of work = 7 days
    100

    ∴ Time taken by them in doing whole work
    =
    100
    × 7
    63

    =
    100
    days
    9

    Respective ratio of time taken by
    A and B in doing the work = 5 : 4
    1
    +
    1
    =
    9
    4x5x100

    5 + 4
    =
    9
    20x100

    ⇒ 20x = 100 ⇒ x = 5
    ∴ Required time
    = 4 × 5 = 20 days

    Correct Option: A

    Remaining work

    = 1 –
    37
    100

    =
    100 - 37
    =
    63
    100100

    ∴ Time taken by (A + B) in doing
    63
    part of work = 7 days
    100

    ∴ Time taken by them in doing whole work
    =
    100
    × 7
    63

    =
    100
    days
    9

    Respective ratio of time taken by
    A and B in doing the work = 5 : 4
    1
    +
    1
    =
    9
    4x5x100

    5 + 4
    =
    9
    20x100

    ⇒ 20x = 100 ⇒ x = 5
    ∴ Required time
    = 4 × 5 = 20 days