Time & Work

·       Time and Work problems are the prime example of indirect proportion. As we all know that if number of persons are increased then time taken to complete a given work would decrease. In indirect proportion when one variable is increase other would automatically decreased and vice-versa.
·       In this chapter we will all types of problems asked in examination one by one through examples.

Points to Remember:
·       Inverse of the work done in one will give the total time require to complete that work. Hence our primary aim would be to find out work done in one day.
·       If A is twice efficient as B than the ratio of their work done will A: B = 2:1 and so on.

Example:
  A take 5 days to complete a job and B takes 10 days to complete the same job. In how much time they will complete the job together?

Explanation:
            Work done by A in one day = 1/5
            Work done by B in one day = 1/10
            Work done by both together in one day = 1/5 + 1/10
                                                                          = 3/10
            Since inverse of work one in one day gives total time to complete the given job
            Hence, total time taken to complete the job when working together = 10/3 = 3.333 Days.

Example:
A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is ?

Explanation:
            Work done by A in one day = 1/15
            Work done by B in one day = 1/20
            One done in one day when working together = 1/15 + 1/20
                                                                                    = 7/60
            Since they work together for 4 days ,
            Work done in 4 days when working together = 4×7/60
                                                                                    = 7/15
            Fraction of work left = 1- work completed
                                            = 1- 7/15
                                            = 8/15

Example:
A is twice as good a workman as B and together they finish a piece of work in 14 days. A alone can finish the work in?

Explanation:
            Since A is Twice good as B, Hence ratio of work done of A & B = 2:1
            Let, Work done by A alone in one day = x
            Therefore, work done by B alone in one day would be = x/2
            Work done in one day when working together = x + x/2
                                                                              = 3x/2
            Time taken in completing the work = 2/3x = 14(given)
                                                X=1/21
            A alone can finish the work in 21 Days.

Example:
A and B can do piece of work in 12 days; B and C in 15 days; C and A in 20 days. A alone can do the work in?

Explanation:
            One day work of
                                    A+B =1/12
                                    B+C = 1/15
                                    C+A = 1/20
Formula to get one day work of A = ½ [ one day work of (A+B) +one day work of (A+C) - one day work of (B+C) ]
                                               
     =1/2 [ 1/12  + 1/15  -1/20 ]
                                                = 1/30
Hence A alone can finish work in 30 days

Example:
A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will do it in ?

Explanation:
One day work of
                        A+B = 1/8 ……..(1)
                        B+C = 1/12 …….(2)
                    A+B+C = 1/6 …….(3)
                       
     2×Eqn(1) – [Eqn (2) + Eqn (1)]


This will give work done in one day by A & C together = 1/8

Hence, Time taken by A & C to complete the work = 8 days.
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