Time and Work

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  1. If 10 people can do a job in 20 days, then 20 people with twice the efficiency can do the same job in








  1. View Hint View Answer Discuss in Forum

    In second case, the efficiency of a man is twice to that in the first case.
    ∴ M1D1 = 2 M2D2
    ⇒ 10 × 20 = 2 × 20 × D2

    ⇒ D2 =
    10 × 20
    		= 5 days
    2 × 20

    Correct Option: A

    In second case, the efficiency of a man is twice to that in the first case.
    ∴ M1D1 = 2 M2D2
    ⇒ 10 × 20 = 2 × 20 × D2

    ⇒ D2 =
    10 × 20
    		= 5 days
    2 × 20

  1. Shashi can do a piece of work in 20 days. Tanya is 25% more efficient than Shashi. The number of days taken by Tanya to do the same piece of work is :








  1. View Hint View Answer Discuss in Forum

    Time taken by Shashi in doing 1 work = 20 days
    Tanya is 25% more efficient than Shashi.
    ∴ Time taken by Tanya

    =
    100
    		× 20 = 16 days
    125

    Correct Option: B

    Time taken by Shashi in doing 1 work = 20 days
    Tanya is 25% more efficient than Shashi.
    ∴ Time taken by Tanya

    =
    100
    		× 20 = 16 days
    125

  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

  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. 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