Time and Work


  1. A can do a piece of work in 6 days. B is 25% more efficient than A. How long would B alone take to finish this work?









  1. View Hint View Answer Discuss in Forum

    Ratio of A's and B's efficiency = 4 : 5
    Ratio of time taken = 5 : 4

    ∴ Time taken by B =
    6 × 4
    5

    =
    24
    = 4
    4
    days
    55

    Aliter : Using Rule 17,
    Here, x = 6, R = 25%
    Time taken by B
    = x ×
    100
    days
    100 + R

    = 6 ×
    100
    125

    = 6 ×
    4
    5

    =
    24
    = 4
    4
    days
    55

    Correct Option: A

    Ratio of A's and B's efficiency = 4 : 5
    Ratio of time taken = 5 : 4

    ∴ Time taken by B =
    6 × 4
    5

    =
    24
    = 4
    4
    days
    55

    Aliter : Using Rule 17,
    Here, x = 6, R = 25%
    Time taken by B
    = x ×
    100
    days
    100 + R

    = 6 ×
    100
    125

    = 6 ×
    4
    5

    =
    24
    = 4
    4
    days
    55


  1. To do a certain work, B would take time thrice as long as A and C together and C twice as long as A and B together. The three men together complete the work in 10 days. The time taken by A to complete the work separately is









  1. View Hint View Answer Discuss in Forum

    Using Rule 2 and 3,
    If B does the work in 3x days, (A + C) will do the same work in xdays.
    If C does that work in 2y days.(A + B) will do it in y days.

    1
    +
    1
    =
    1
    x3x10

    4
    =
    1
    3x10

    ⇒ 3x = 40
    ⇒ x =
    40
    3

    Again,
    1
    +
    1
    =
    1
    y2y10

    3
    =
    1
    2y10

    ⇒ y =15
    ∴ (A + B + C)’s 1 day’s work
    =
    1
    10

    1
    +
    1
    +
    1
    =
    1
    A403010

    1
    =
    1
    -
    1
    -
    1
    A104030

    =
    12 - 3 - 4
    =
    5
    =
    1
    12012024

    ∴ A alone will complete the work in 24 days.

    Correct Option: B

    Using Rule 2 and 3,
    If B does the work in 3x days, (A + C) will do the same work in xdays.
    If C does that work in 2y days.(A + B) will do it in y days.

    1
    +
    1
    =
    1
    x3x10

    4
    =
    1
    3x10

    ⇒ 3x = 40
    ⇒ x =
    40
    3

    Again,
    1
    +
    1
    =
    1
    y2y10

    3
    =
    1
    2y10

    ⇒ y =15
    ∴ (A + B + C)’s 1 day’s work
    =
    1
    10

    1
    +
    1
    +
    1
    =
    1
    A403010

    1
    =
    1
    -
    1
    -
    1
    A104030

    =
    12 - 3 - 4
    =
    5
    =
    1
    12012024

    ∴ A alone will complete the work in 24 days.



  1. P is thrice as good a workman as Q and therefore able to finish a job in 48 days less than Q. Working together, they can do it in :









  1. View Hint View Answer Discuss in Forum

    Using Rule 2,
    Let time taken by P = x days
    Then, time taken by Q = 3x days
    ∴ 3x – x = 48 ⇒ x = 24
    ∴ (P + Q)’s 1 day’s work

    1
    +
    2
    =
    3 + 1
    =
    1
    24727218

    ∴ Required time = 18 days

    Correct Option: A

    Using Rule 2,
    Let time taken by P = x days
    Then, time taken by Q = 3x days
    ∴ 3x – x = 48 ⇒ x = 24
    ∴ (P + Q)’s 1 day’s work

    1
    +
    2
    =
    3 + 1
    =
    1
    24727218

    ∴ Required time = 18 days


  1. A and B can do a job together in 12 days. A is 2 times as efficient as B. In how many days can B alone complete the work ?









  1. View Hint View Answer Discuss in Forum

    Using Rule 2,
    If A alone completes the work in x days, B will complete the same in 2x days.

    1
    +
    1
    =
    1
    x2x12

    =
    2 + 1
    =
    1
    2x12

    ⇒ 2x = 36
    ∴ B alone will complete the work in 36 days (i.e. 2x ).

    Correct Option: C

    Using Rule 2,
    If A alone completes the work in x days, B will complete the same in 2x days.

    1
    +
    1
    =
    1
    x2x12

    =
    2 + 1
    =
    1
    2x12

    ⇒ 2x = 36
    ∴ B alone will complete the work in 36 days (i.e. 2x ).



  1. A can do a certain work in 12 days. B is 60% more efficient than A. How many days will B and A together take to do the same job?









  1. View Hint View Answer Discuss in Forum

    Time taken by B in completing the work

    = 12 ×
    100
    =
    15
    days
    1602

    ∴ (A+B)’s 1 day’s work
    1
    +
    2
    =
    5 + 8
    =
    13
    12156060

    Hence, the work will be completed in
    60
    days
    13

    Aliter : Using Rule 17,
    Here, x = 12, R = 60%
    Time taken by B
    = x ×
    100
    days
    100 + R

    = 12 ×
    100
    days
    160

    =
    15
    days
    2

    Now using Rule 2,
    Time taken by A and B
    =
    xy
    x + y

    =12 ×
    15
    2
    12 ×
    15
    2

    =
    12 × 15
    =
    60
    days
    3913

    Correct Option: D

    Time taken by B in completing the work

    = 12 ×
    100
    =
    15
    days
    1602

    ∴ (A+B)’s 1 day’s work
    1
    +
    2
    =
    5 + 8
    =
    13
    12156060

    Hence, the work will be completed in
    60
    days
    13

    Aliter : Using Rule 17,
    Here, x = 12, R = 60%
    Time taken by B
    = x ×
    100
    days
    100 + R

    = 12 ×
    100
    days
    160

    =
    15
    days
    2

    Now using Rule 2,
    Time taken by A and B
    =
    xy
    x + y

    =12 ×
    15
    2
    12 ×
    15
    2

    =
    12 × 15
    =
    60
    days
    3913