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Note on Time and Work

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The unitary method is a method or technique in an algebra for solving a class of problems in variation.Time and work are also related to the unitary method. Here, we calculate the part of a work in unit time and also calculate the time taken to do a work.

  • Work from Days:
    If A can do a piece of work in n days, then A's 1 day's work =\(\frac{1}{n}\)

  • Days from Work:
    If A's 1 day's work = \(\frac{1}{n}\),then A can finish the work in n days.

  • Ratio:
    If A is thrice as good workman as B, then:
    The ratio of work done by A and B = 3: 1.
    The ratio of times taken by A and B to finish a work = 1: 3.
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  • No. of days = total work / work done in 1 day

  • Relationship between Men and Work
    More men —can do → More work
    Less men —can do →Less work

  • Relationship between Work and Time
    More work —takes →More Time
    Less work —takes →Less Time

  • Relationship between Men and Time
    More men —can do in →Less Time
    Less men —can do in →More Time

  • A complete work is considered as 1.
  • Work done by A in unit time added to the work done by B in unit time, gives the time work done by A and B together in unit time.
  • The work done by A in unit time is subtracted from the work done by A and B together works in unit time gives the work done by B in unit time.
  • Total work is done in different steps is always 1.
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Very Short Questions

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  • Short questions By selling a radio with 25% profit, the profit amount is Rs 60 for how much price was it sold? If a carpet that cost Rs 4500 is sold at a profit of 30%, what is the selling price ? A watch was bought for Rs 3405.50. At what price should it be sold to gain Rs 120. Bijay bought an old house for Rs 220,000 and spend Rs 83,500 for its repair and decoration. If he sold the house for Rs 300,000 find his loss percentage. A radio is sold for Rs 2700, there is a loss of 10% at what price should it be sold to gain 712%. What percent of discount should be given in a doll costing Rs. 180 such that a customer has to buy it for Rs 160? At 18% loss the selling price of an articles is Rs 164. Calculate the cost price of the article. How much should you have to pay to buy the volleyball shown in the figure?

  •  A and B can do a piece of work in 15 and 20 days respectively. After working  4 days together, B left and A complete the remaining works. How any days the remaining work completed? 

    15 days
    2 days
    20 days 
    8 days
  •  A and B can finish a piece of work in 16 and 24 days respectively.They worked together for 6 days and A left the job. In how many days B can complete the  remaining work?

    13 days 


    18 days 


    9 days


    20 days 


  • Sakar can do a work in 24 days and Bivas can do the same work in 30 days. They worked together for 8 days then Sakar goes away. In how many days will Bivas finish the remaining work ?

    10 days 


    16 days 


    12 days 


    14 days 


  • Shiva and Bishnu can do a piece of work in 12 days. Shiva alone can do it  in 18 days. Both start the work together but Shiva leaves after 6 days. How long Bishnu work to finish the remaining work ?

    18 days 


    24 days 


    22 days 


    26 days 


  • Beena and Meena together can do a piece of work in 12 days. Meena  alone can finish the work in 18 days. If she leaves after working alone for 6 days, in how many days will Beena finish the remaining work?

    20 days 


    22 days 


    18 days 


    12 days 


  • Bimila and Sharda can do a piece of work in 8 days. Bimala alone can do that work in 12 days. If Bimila worked alone for 4 days and stopped to do, how long will Sharda take to complete the remaining work? 

    18 days 
    15 days 
    23 days 
    16 days 
  • A and B can finish a piece of work in 40 days. after they worked for 25 days ,B left.If a can finish the remaining work in 45 days, how long will B alone take to finish the whole work?

    50 days 


    45 days 


    60 days 


    40 days 


  • A can do a piece of work in 18 days and B in 24 days. They both worked together and after some days A left. If B finished the remaining work in 3 days, for how long did A work together?

    9 days 


    12 days 


    18 days 


    15 days 


  •  A and B can do a piece of work in 30 and 45 days respectively. They work it together for some days then B leaves. If B leaves 5 days before the completion of the work, for how many days did they work together ?

    15 days 


    21 days 


    17 days 


    10 days 


  • A and B together can finish a work in 36 days. If A can do as much in 4 days as B can do it 9 days, how long would each take to do work alone?

    50,115 days 


    51,116 days 


    55,117 days 


    52,117 days 


  • X, Y and Z can do a piece of work in 20 days working together.Y can do the same work in 60 days and Z can do it in 120 days. In how many days X can do the whole work alone?

    30 days 


    45 days 


    35 days 


    40 days 


  • A, B and C can do a piece of work in 30, 40, and 60 days respectively. All of them started the work together but B left after working for 8 days. In how many days A and C can complete the remaining work?

    11 days


    10 days 


    8days 


    5 days 


  • A man undertakes to do a certain job in 32 days. He hires 12 men for the job. At the end  of 8 days, only one-fifth of the work was completed. How many extra men must be employed in order to complete the work in time?

    3 men 


    4 men 


    6 men 


    5 men 


  • 10 workers can do a work in 20 days, when they start the work, after how many days should 5 workers leave the work so that the work would be finished in 35 days?

    10 days 


    8 days 


    5 days 


    3 days 


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DISCUSSIONS ABOUT THIS NOTE

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Answer

A ,B,C together can do a piece of work in 6days.B alone can do it in 26 days and B and C together can do it in 10 days.in how many days could A and B together finish it?


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Shajan

A can do a piece of work in 6 days and B can do in 8 days. A and B work together on it in alternative days B in the beginning. In how many days would the work be finished?


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reshma

A did 60% of a work in 36 days and then gets B to help him. They work togeher for 6 days and B leaves. If A finishes the remaining work in 15 days, how ;ong would it take Bto do the whole work?


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