Time and Work


  1. 4 mat-weavers can weave 4 mats in 4 days. At the same rate how many mats would be woven by 8 mat-weavers in 8 days ?









  1. View Hint View Answer Discuss in Forum

    Using Rule 1,

    4 : 8
    : : 4 : x
    4 : 8

    where, x is no. of mats
    ⇒ 4 × 4 × x = 8 × 8 × 4
    ∴ x =
    8 × 8 × 4
    = 16
    4 × 4

    Correct Option: D

    Using Rule 1,

    4 : 8
    : : 4 : x
    4 : 8

    where, x is no. of mats
    ⇒ 4 × 4 × x = 8 × 8 × 4
    ∴ x =
    8 × 8 × 4
    = 16
    4 × 4


  1. 5 persons can prepare an admission list in 8 days working 7 hours a day. If 2 persons join them so as to complete the work in 4 days, they need to work per day for :









  1. View Hint View Answer Discuss in Forum

    Using Rule 1,
    More persons, less working hours/day
    Less days, more working hours/day

    Persons   7 : 5
    : : 7 : x
    Days   4 : 8

    where, x is hours/days
    ∴ 7 × 4 × x = 5 × 8 × 7
    ∴ x =
    5 × 8 × 7
    = 10 hours
    7 × 4

    Correct Option: A

    Using Rule 1,
    More persons, less working hours/day
    Less days, more working hours/day

    Persons   7 : 5
    : : 7 : x
    Days   4 : 8

    where, x is hours/days
    ∴ 7 × 4 × x = 5 × 8 × 7
    ∴ x =
    5 × 8 × 7
    = 10 hours
    7 × 4



  1. A wall of 100 metres can be built by 7 men or 10 women in 10 days. How many days will 14 men and 20 women take to build a wall of 600 metres ?









  1. View Hint View Answer Discuss in Forum

    Using Rule 1,
    7 men ≡ 10 women

    or 1 man
    10
    women
    7

    14 men + 20 women
    =
    10 × 14
    + 20women
    7

    = 40 women
    Now, more work, more days
    More women, less days
    Work   1 : 6
    : : 10 : x
    Women   40 : 10

    Where x = number of days
    ⇒ 1 × 40 × x = 6 × 10 × 10
    or x =
    600
    = 15
    40

    Correct Option: A

    Using Rule 1,
    7 men ≡ 10 women

    or 1 man
    10
    women
    7

    14 men + 20 women
    =
    10 × 14
    + 20women
    7

    = 40 women
    Now, more work, more days
    More women, less days
    Work   1 : 6
    : : 10 : x
    Women   40 : 10

    Where x = number of days
    ⇒ 1 × 40 × x = 6 × 10 × 10
    or x =
    600
    = 15
    40


  1. If 72 men can build a wall of 280 m length in 21 days, how many men could take 18 days to build a similar type of wall of length 100 m?









  1. View Hint View Answer Discuss in Forum

    Using Rule 1,
    We know that

    W1
    =
    W2
    M1D1M2D2

    280
    =
    100
    72 × 21x × 18

    Where x = number of men
    ⇒ x × 18 × 280 = 100 × 72 × 21
    ⇒ x =
    100 × 72 × 21
    = 30
    18 × 280

    Correct Option: A

    Using Rule 1,
    We know that

    W1
    =
    W2
    M1D1M2D2

    280
    =
    100
    72 × 21x × 18

    Where x = number of men
    ⇒ x × 18 × 280 = 100 × 72 × 21
    ⇒ x =
    100 × 72 × 21
    = 30
    18 × 280



  1. 39 persons can repair a road in 12 days working 5 hours a day. In how many days will 30 persons working 6 hours a day complete the work ?









  1. View Hint View Answer Discuss in Forum

    Less persons, more days (Indirect)
    More working hours/day, less days (Indirect)
    Let required no. of days be x.

    30 : 39
    : : 12 : x
    6 : 5

    ⇒ 30 × 6 × x = 39 × 5 × 12
    ⇒ x =
    39 × 5 × 12
    = 13 days
    30 × 6

    Aliter : Using Rule 1,
    Here, M1 = 39, D1 = 12, T1 = 5
    M2 = 30, D2 = ?, T2 = 6
    M1D1T1 = M2D2T2
    39 × 12 × 5 = 30 × D2 × 6
    ⇒ D2 =
    39 × 12 × 5
    = 13 days
    30 × 6

    Correct Option: B

    Less persons, more days (Indirect)
    More working hours/day, less days (Indirect)
    Let required no. of days be x.

    30 : 39
    : : 12 : x
    6 : 5

    ⇒ 30 × 6 × x = 39 × 5 × 12
    ⇒ x =
    39 × 5 × 12
    = 13 days
    30 × 6

    Aliter : Using Rule 1,
    Here, M1 = 39, D1 = 12, T1 = 5
    M2 = 30, D2 = ?, T2 = 6
    M1D1T1 = M2D2T2
    39 × 12 × 5 = 30 × D2 × 6
    ⇒ D2 =
    39 × 12 × 5
    = 13 days
    30 × 6