Time and Work

  1. A alone can complete a piece of work in 15 days and B & C together can complete the same work in 8 1/3 days. B is 100% more efficient than C. How many days is required to complete the work if A and C work together ?
    12 days
    8 days
    6 days
    9 3/8 days
    5 days
    Option D
    LCM of 15 and 8 1/3 days = 75
    efficiency of A = 75/15 = 5
    efficiency of B and C = 75 * 3/25 = 9
    let efficiency of C = 100
    efficiency of B = 200
    ratio of efficiency of B and C = 2 : 1
    efficiency of B = 9 * 2/3 = 6
    efficiency of C = 9 * 1/3 = 3
    time = 75/(5 + 3) = 75/8 = 9 3/8 days

     

  2. Rajat alone can complete a piece of work in ‘x’ days and Sujit alone can complete the same work in (x + 5) days. If they together can complete the same work in 6 days, then find in how days Sujit can complete the whole work ?
    10 days
    6 days
    8 days
    5 days
    15 days
    Option E
    1/x + 1/x + 5 = 1/6
    2x + 5 / x^2 + 5x = 1/6
    x^2 + 5x = 12x + 30
    x^2 – 7x – 30 = 0
    x = 10 , – 3
    Days can not come in negative, so that value of x = 10
    Days taken by Sujit to complete the work = x + 5 = 15 days

     

  3. A alone can complete a work in 25 days and B alone can complete same work in 45 days. How many days are taken by A and B together to complete 60% of work ?
    14 days
    135/14 days
    68/7 days
    18/5 days
    9 2/5 days
    Option B
    LCM of 25 and 45 = 225
    efficiently of A = 225/ 25 = 9
    efficiently B = 225/45 = 5
    days = 225/14 * 60/100 = 135/14 days

     

  4. A and B can complete a work in 24 days and B and C together can complete the same work in 30 days. A and C together work for 15 days and after 15 days A and C left the work, remaining work done by alone B. If the efficiency ratio of A and B is 2 : 3, then find in how many days total work will be completed ?
    28 days
    60 days
    40 days
    38 days
    25 days
    Option C
    LCM of 24 and 30 = 120
    total work = 120
    efficiency of A and B = 120/24 = 5
    efficiency of B and C = 120/30 = 4
    efficiency of A = 5 * 2/5 = 2
    efficiency of B = 5 – 2 = 3
    efficiency of C = 4 – 3 = 1
    A and C together work for 15 days = (2 + 1) * 15 = 45
    remaining work = 120 – 45 = 75
    days required to complete remaining work = 75/3 = 25 days
    total days = 15 + 25 = 40days

     

  5. P , Q and R together can complete a work in 20 days and the ratio of time taken by P , Q and R is 8 : 6 : 3. How many days is taken by Q and R together to complete the whole work ?
    18 days
    25 days
    26 days
    30 days
    32 days
    Option B
    Time ratio of P , Q and R = 8 : 6 : 3
    LCM of 8, 6 and 3 = 24
    efficiency ratio of P, Q and R = 24/8 : 24/6 : 24/3 = 3 : 4 : 8
    let efficiency of P , Q and R = 3x , 4x and 8x respectively.
    total work = 20 ( 3x + 4x + 8x ) = 300x
    time taken by Q and R together complete the work = 300x / 12x = 25 days

     

  6. The efficiency of Rohit is 40% more than Suraj. If Suraj alone can do a work in 14 days, then find how many days is taken by Rohit to complete the whole work ?
    10 days
    15 days
    22 days
    13 days
    18 days
    Option A
    Efficiency of Suraj = 5x
    Efficiency of Rohit = 5x * 140/100 = 7x
    total work = 14 * 5x = 70x
    time taken by Rohit to complete the work = 70x/7x = 10 days

     

  7. A and B can do a work in 10 days B and C can do the same work in 12 days and A and C can do the same work in 15 days. How many days by A, B and C together to complete total work ?
    5 days
    8 days
    14 days
    15 days
    6 days
    Option B
    LCM of 10 , 12 and 15 = 60
    efficiency of A and B = 60/10 = 6
    efficiency of B and C = 60/12 = 5
    efficiency of A and C = 60/15 = 4
    A + B + B + C + A + C = 15
    A + B + C = 7.5
    time = 60/7.5 = 8 days

     

  8. 12 men do a work in 18 days. They started work together and after 8 days, 3 more joined with them. In how many days the remaining work will be completed ?
    8 days
    9 days
    12 days
    18 days
    15 days
    Option A
    Let the remaining work completed in ‘x’ days
    12 * 18 = (12 * 8) + (15 * x)
    15x = 120
    x = 8 days

     

  9. Rita , Gita and Sita can do a piece of work in 24 days , 20 days and 15 days respectively. If they got total wages of rs. 3800, then find difference between the wages got by Sita and Gita.
    500
    800
    480
    400
    620
    Option D
    LCM of 24 , 20 and 15 = 120
    total work = 120
    efficiency of Rita = 120/24 = 5
    efficiency of Gita = 120/20 = 6
    efficiency of Rita = 120/15 = 8
    difference = 3800 * 8 – 6/19 = rs.400

     

  10. If 12 men can complete a piece of work in 20 days and 15 women can complete the same work in 24 days, then in how many days 8 men and 8 women can complete the whole work ?
    15 days
    18 days
    17 days
    12 days
    24 days
    Option B
    12 men * 20 days = 15 women * 24 days
    m/w = 3/2
    total work = 12 * 3 * 20 = 720
    time = 720 / (8 * 3 + 8 * 2 ) = 720/40 = 18 days

     

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