Time and Work


  1. Twenty women together can complete a work in 16 days. 16 men together can complete the same work in 15 days. The ratio of the working capacity of a man to that of a woman is :









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    20 × 16 women ≡ 16 × 15 men
    ⇒ 4 women ≡ 3 men

    men
    =
    4
    women3

    Hence, working capacity of man : woman = 4 : 3

    Correct Option: B

    20 × 16 women ≡ 16 × 15 men
    ⇒ 4 women ≡ 3 men

    men
    =
    4
    women3

    Hence, working capacity of man : woman = 4 : 3


  1. A contractor undertakes to make a road in 40 days and employs 25 men. After 24 days, he finds that only one-third of the road is made. How many extra men should he employ so that he is able to complete the work 4 days earlier?









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    Scheduled time to complete the work = 40 days

    25 men in 24 days do
    1
    work
    3

    ∴ 1 man in 1 day does
    1
    =
    1
    work.
    3 × 25 × 241800

    Work remaining
    = 1 -
    1
    =
    2
    33

    The work is to be completed 4 days before schedule i.e., in (40 – 4) 36 days
    No. of days left for
    2
    rd work
    3

    = 36 – 24 = 12 days
    1
    1800

    work is done in 1 day by 1 man.
    2
    work will be done in 12 days by
    3

    1800 ×
    2
    ×
    1
    = 100 men
    312

    25 men are already working
    ∴ Extra men to be employed
    = 100 – 25 = 75

    Correct Option: C

    Scheduled time to complete the work = 40 days

    25 men in 24 days do
    1
    work
    3

    ∴ 1 man in 1 day does
    1
    =
    1
    work.
    3 × 25 × 241800

    Work remaining
    = 1 -
    1
    =
    2
    33

    The work is to be completed 4 days before schedule i.e., in (40 – 4) 36 days
    No. of days left for
    2
    rd work
    3

    = 36 – 24 = 12 days
    1
    1800

    work is done in 1 day by 1 man.
    2
    work will be done in 12 days by
    3

    1800 ×
    2
    ×
    1
    = 100 men
    312

    25 men are already working
    ∴ Extra men to be employed
    = 100 – 25 = 75



  1. Working efficiencies of P and Q for completing a piece of work are in the ratio 3 : 4. The number of days to be taken by them to complete the work will be in the ratio









  1. View Hint View Answer Discuss in Forum

    Using Rule 15,
    Efficiency and time taken are inversely proportional.
    ∴ Required ratio = 4 : 3

    Correct Option: D

    Using Rule 15,
    Efficiency and time taken are inversely proportional.
    ∴ Required ratio = 4 : 3


  1. A can do a work in 12 days. When he had worked for 3 days, B joined him. If they complete the work in 3 more days, in how many days can B alone finish the work?









  1. View Hint View Answer Discuss in Forum

    Let B alone do the work in x days.

    ∴ 6 ×
    1
    + 3 ×
    1
    = 1
    12x

    1
    +
    3
    = 1
    2x

    3
    =
    1
    ⇒ x = 6 days
    x2

    Correct Option: A

    Let B alone do the work in x days.

    ∴ 6 ×
    1
    + 3 ×
    1
    = 1
    12x

    1
    +
    3
    = 1
    2x

    3
    =
    1
    ⇒ x = 6 days
    x2



  1. A road of 5 km length will be constructed in 100 days. So 280 workers were employed. But after 80 days it was found that only
    3
    1
    km road was completed.
    2

    Now how many more people were needed to finish the work in the specified time ?









  1. View Hint View Answer Discuss in Forum

    Using Rule 1,
    Remaining work

    = 5 –
    7
    =
    3
    22

    M1 × D1 × W2 = M2 × D2 × W1
    ⇒ 280 × 80 ×
    3
    2

    = M2 × 20 ×
    7
    2

    ⇒ M2 =
    280 × 80 × 3
    = 480
    20 × 7

    ∴ Required number of additional men = 480 – 280 = 200

    Correct Option: C

    Using Rule 1,
    Remaining work

    = 5 –
    7
    =
    3
    22

    M1 × D1 × W2 = M2 × D2 × W1
    ⇒ 280 × 80 ×
    3
    2

    = M2 × 20 ×
    7
    2

    ⇒ M2 =
    280 × 80 × 3
    = 480
    20 × 7

    ∴ Required number of additional men = 480 – 280 = 200