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Time Work & Wages Test 477
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Time Work & Wages Test 477
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  • Question 1/10
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    A and B alone can do a piece of work in 4 and 9 days, respectively. In how many days will the work be completed, if they both work on alternate days, starting with B?
    Solutions
    A and B alone can do a piece of work in 4 and 9 days, respectively.

    Total work = LCM of 4 and 9 = 36 units

    Efficiency of A = 36/4 = 9

    Efficiency of B = 36/9 = 4

    They both work on alternate days, starting with B.

    Work done by B and A in first two days

    = 4 + 9 = 13 units

    2 days 13 units

    4 days 26 units

    Work done by B on 5th day = 4 units

    Remaining work = 36 – 26 – 4 = 6 units

    Time taken by A to do remaining work = 6/9 = 2/3 days

    Total time = 5 + 2/3

    = 5 days

    Hence, option B is the correct answer.

  • Question 2/10
    1 / -0.25

    In a company, a piece of work can be completed in 4, 6 and 18 days alone by R, S andT, respectively. In how many days will the work be completed if they work together?(Rounded off to 2 decimal places)
    Solutions
    In a company, a piece of work can be completed in 4, 6 and 18 days alone by R, S andT, respectively.

    Total work = LCM of 4, 6 and 18 = 36 units

    Efficiency of R = 36/4 = 9

    Efficiency of S = 36/6 = 6

    Efficiency of T = 36/18 = 2

    Time taken by them together to complete the work

    = 36/[9 + 6 + 2]

    = 2.12 days

    Hence, option B is the correct answer.

  • Question 3/10
    1 / -0.25

    A and B can do a piece of work in 5 days and 10 days, respectively. They began the work together but A left after some days and B finished the remaining work in 8 days. After how many days did A leave?
    Solutions
    A and B can do a piece of work in 5 days and 10 days, respectively.

    Total work = LCM of 5 and 10 = 10 units

    Efficiency of A = 10/5 = 2

    Efficiency of B = 10/10 = 1

    Work done by B in 8 days = 1(8) = 8 units

    Remaining work = 10 – 8 = 2 units

    Time taken by A and B to complete the 2 units work

    = 2/(2+1) = 2/3 days

    A leave the work after 2/3 days.

    Hence, option A is the correct answer.

  • Question 4/10
    1 / -0.25

    A can complete a work in 18 days, while B can complete it in 12 days. B worked on it for 4 days. How long will A take to finish the remaining work?
    Solutions
    A can complete a work in 18 days, while B can complete it in 12 days.

    Total work = LCM of 18 and 12 = 36 units

    Efficiency of A = 36/18 = 2

    Efficiency of B = 36/12 = 3

    Work done by B in 4 days = 3(4) = 12 units

    Remaining work = 36 – 12 = 24 units

    Time taken by A to complete the remaining work

    = 24/2 = 12 days

    Hence, option B is the correct answer.

  • Question 5/10
    1 / -0.25

    X and Y can complete a work in 9 days and 36 days, respectively. X begins to do the work and they work alternately one at a time for one day each. The whole work will be complete in:
    Solutions

    Time taken by X = 9 days

    Time taken by Y = 36 days

    Total work = L.C.M(9,  36) = 36 units

    Efficiency of X = 36/9 = 4 units

    Efficiency of Y = 36/36 = 1 unit

    According to question,

    (X+Y) 2 days work = 4 + 1 = 5 units

    (X+Y) 14 days work = 5 ×

    Remaining work = 36 – 35 = 1 unit

    Time taken by X to complete the remaining work = 1/4 days

    Total time taken = 14 +1/4 = days

    Hence, option D is the correct answer.

  • Question 6/10
    1 / -0.25

    4 women or 6 boys can finish a work in the same number of days. A boy can finish it in 60 days. In how many days can 5 women finish the work, working together every day?
    Solutions

    Given,

    4 women = 6 boys

    Ratio of efficiences of a woman and a boy = 3 : 2

    Total work = 2 × 60 = 120 days

    Time taken by 5 women = 120/(5×3) = 8 days 

    Hence, option C is the correct answer.

  • Question 7/10
    1 / -0.25

    P and Q together can complete a work in 20 days. If Q alone can complete the work in 25 days, then in how many days P alone can complete the same work?
    Solutions

    Let the total work be 100 units(LCM of 20 and 25).

    Efficiency of (P +Q) = 100/20 = 5 units/day

    Efficiency of P = 100/25 = 4 units/day

    Efficiency of Q = 5 – 4 = 1 unit/day

    Time taken by Q alone to complete the work = 100/1 = 100 days

    "Hence, option B is the correct answer."

  • Question 8/10
    1 / -0.25

    60 men can complete a work in 40 days. They start work together but after every 10 day, 5 men leave the work. In how many days will the work be completed?

    Solutions

    Total work = 60 × 40 = 2400 units

    First 10 days work done by 60 men = 60 × 10 = 600 units

    Next 10 days work done by 55 men = 55 × 10 = 550 units

    Next 10 days work done by 50 men = 50 × 10 = 500 units

    Next 10 days work done by 45 men = 45 × 10 = 450 units

    Remaining work = 2400 – (600 + 550 + 500 + 450) = 2400 – 2100 = 300 units

    Time taken by 40 men to complete the remaining work =  = 7.5 days

    Total time = 10 + 10 + 10 + 10 + 7.5 = 47.5 days

    Hence, option A is the correct answer.

  • Question 9/10
    1 / -0.25

    At a construction site, Raju can paint a wall in 36 hours, while Angad can do the same work in 18 hours. Sumit can paint the same wall in 24 hours. In how much time can they paint the wall if they all work together?

    Solutions

    Let the total work be 72 units(LCM of 36,18 and 24)

    Efficiency of Raju = 72/36 = 2 units/hour

    Efficiency of Angad = 72/18 = 4 units/ hour

    Efficiency of Sumit = 72/24 = 3 units/ hour

    Total efficiency of Raju, Angad and Sumit = 2 + 4 + 3 = 9 units/ hour

    Required time = 72/9 = 8 hours

    Hence, option D is the correct answer.

  • Question 10/10
    1 / -0.25

    Aarush and Maahi together can do a piece of work in 10 days. If Aarush alone can do the same work in 15 days, then how many days Maahi alone will take to do the same work?
    Solutions

    Let the total work be 30 units(LCM of 10 and 15)

    Efficiency of Aarush and Maahi = 30/10 = 3 units/day

    Efficiency of Aarush = 30/15 = 2 units/day

    Efficiency of Maahi = 3 – 2 = 1 units/day

    Time taken by Maahi to complete the work = 30/1 = 30 days

    Hence, option C is the correct answer.

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