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 1/10th part of the total work. On the other hand, if a man completes 1/10th of the work in one day, then he will take 10 days to complete the work. Thus, we obtain the following rules:
Rule 1 If a person X completes a piece of work in n days, then work done by person X in one day is \( (1/n)^th \) part of the work.
Rule 2 If a person X completes \( (1/n)^th \) part of the work in one day, then person X will take n days to complete the work.
In this chapter, we shall mainly discuss two types of problems on time and work.
(i) On finding the time required to complete a piece of work.
(ii) On finding the work done in a given period of time.
Example : Kami, Karya and Kirti can together weave a carpet in 4 days. Kami by herself can weave the same sized carpet in 12 days and Kirti can do it in 10 days How long will Karya take to do the work by herself?
Solution :
Time taken by Kami, Karya and Kirti to weave the carpet = 4 days.
Time taken by Kami to weave the carpet = 12 days
and, Time taken by Kirti to weave the carpet = 10 days.
Kami, Karya and Kirti’s 1 day’s work = ¼
Kamis 1 days work = 1/12 and Kirtis 1 days work = 1/12
Karya’s 1 day’s work = (Kami, Karya and Kirti’s I day’s work) – (Kami’s 1 day’s work) – (Kirti’s 1 days work )
\( = 1/4 – 1/12 -1/10 = 15-5-6/60 = 4/60 = 1/15 \)Hence, Karya can weave the carpet in 15 days.