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Maths / Direct and Inverse Variation / Time and Work
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Time and Work

As we all know that the amount of work done by a person varies directly with the time taken by him (her) to complete it .Thus, if a man can complete a piece of work in 10 days, then by unitary method,we can say that in one day he will do only  frac{1}{10} th part of the total work. On the other hand ,if a man completes  frac{1}{10} th of the work in one day , he will take 10 days to complete the work .Thus, we obtain the following rules:

  • Rule1: If a person x complete a piece of work in n days, then work done by person x in one day is large frac{1}{n}th part of the work .
  • Rule2: If a person x completes large frac{1}{n}th  part of the work in one day , then person x will taken n days to complete the work .
  • Illustration: Together, Chandu and Monu plough a field in 4 days . Monu alone takes 6 days to plough the same field .In how many days can Chandu alone plough the field ?

    Solution: We have, time taken by Chandu and Monu plough the field together = 4 days.

    Time taken by Monu to plough the field = 6 days. Chandu and Monu 1 day work = frac{1}{4}

    Monu 1 day work = frac{1}{6} .  Now,  Chandu 1 day works = (Chandu and Monu 1 days work ) - (Monu 1 days work )

    =frac{1}{4} ;- frac{1}{6}; = frac{3-2}{12}=frac{1}{12}

    Hence, Chandu can plough the field in 12 days.

    Illustration: A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days. In how many days will they finish it together and separately?

    Solution: We have, A and B can do a piece of work in 12 days; B and C in 15 days; C and A in 20 days

    So, A and B's 1 day's work = frac{1}{12}      ..............................(1)

    B and C's 1 day's work = frac{1}{15}           ..............................(2)

    C and A's 1 day's work = frac{1}{20}           ..............................(3)

    Adding equations (1), (2), (3) we have

    2(A + B + C)'s 1 day's work = frac{1}{12}+frac{1}{15}+frac{1}{20}=frac{5+4+3}{60}=frac{12}{60}

                                             =frac{1}{5}

    Hence, (A + B + C)'s 1 day's work =frac{1}{2times 5}

    (A + B + C)'s 1 day's work = frac{1}{10}

    Hence, A, B and C together can finish the work in 10 days.

    Now,

    A's 1 day's work = (A, B,and C's 1 day's work ) - (B and C's 1 day's work)

                            =frac{1}{10}-frac{1}{15}

                             =frac{3-2}{30}=frac{1}{30}

    So, A alone can finish the work in 30 days.

    Now,

    B's 1 day's work = (A, B,and C's 1 day's work ) - (A and C's 1 day's work)

                             =frac{1}{10}-frac{1}{20}

                              =frac{2-1}{20}=frac{1}{20}

    So, B alone can finish the work in 20 days.

    Now,

    C's 1 day's work = (A, B,and C's 1 day's work ) - (A and B's 1 day's work)

                             =frac{1}{10}-frac{1}{12}

                             =frac{6-5}{60}=frac{1}{60}

    So, C alone can finish the work in 60 days.


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