Time and Work - Shortcut Techniques

Today I am going to share techniques to solve Time and Work question. I have already shared a technique for this chapter here.
time and work


This topic is based on two main concepts:
  • ONE DAY WORK: Unitary Method 
  • TOTAL WORK
Let us pick up a question to understand it .

Question - A can do a piece of work in 10 days and B can do the same work in 15 days. How long will they take to do the work together.Answer - 
              A =10 days
              B = 15 days
             A+B = ? days

To answer we can apply two methods.

According to the first method

If A can do a piece of work in 10 days

A’s one day work = 1/10

Similarly B’s one day work = 1/15

Time and work


So this method says that

⇒ To do 1/6 work (A+B) take = 1 day 

⇒ To do 1 work (A+B) take = 1/ (1/6) = 1 x6/1 = 6 days 

Based on this method , the shortcut would be:
Time and work 2
          
Time and work 3




SECOND METHOD :

A = 10 days

B  = 15 days

⇒ Total work  = 30 units 

WHY 30 units ?

⇒ Remember the LCM of 10 and 15 is 30.

⇒ A does 1 work in 10 days  so in one A will do = 30/10 = 3 units

⇒ B does 1 work in 15 days so in 1 day B will do = 30/15 = 2 units

⇒ So together ( A+B) complete = 3+2 = 5 units in one day


Time and work 5

Now which method to be applied, depends upon the kind of 

questions asked and your comfort level.


Question - A can do a piece of work in 10 days. A and B together take 6 days to complete the work. How long will B take to complete the work?
Solution - 
    Time and work 6

    According to the second method

    Time and work 7


    Time and work 8

    Now according to the third method:

    Time and work 10
    ⇒ Now the LCM of 10 and 6 is 30 .
     Total work = 30 units
    ⇒ A+B take 6 days to complete 30 units
    So in 1 day A+B will complete = 30/6 = 5 units
    Similarly A will complete= 30/10 =3 units 
    ⇒ And therefore B will complete  = 5-3 = 2 units
    Now B completes 2 units in = 1 day
    ⇒ B completes 1 unit in = 1/2 day
    ⇒ B completes 30 units = 1/2×30=15 days 

    The same concept could be applied in different questions of TIME AND WORK.

    Question - A can do a work in 10 days . B can do the same work in 20 days . They both started together but after 2 days A left.The remaining work was done alone by B.How long A and B both took to complete the work?


      Time and work 11
      Work done by A in one day = 1/10

      ⇒So the work done by A in 2 days = 2/10

      Work done by B in one day = 1/20

      Work done by B in 2 days = 2/20

      ⇒ Again work done by B in x days = x/20

      Together they completed 1 work



      Time and work 13


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