Time and Work Concept of Efficiency

Time and work

This chapter based on relationship between time and work. As it is very clear to all of us that the work is directly related with time. As one can say if a particular person or machine works for more time then more work will be done and if it devoted less time then it yields less work i.e., output of a machine or person is directly proportional to time, provided the he/she maintained his/her efficiency during the work.

Concept of Efficiency

Suppose a person can complete a particular work in 2 days then we can say that each day he does half of the work or 50% work each day. This is clear that his efficiency is 50% per day.

Now, if a person can complete a work in n days then his one day’s work = 1/n

And this one day’s work in terms of percentage is called his efficiency.

Also if a person can complete 1/n work in one day, then he can complete the whole work in n days.

Relation between work of 1 unit of time and percentage efficiency.

A person can complete his work in n days, then his one days work = 1/n, his percentage efficiency = 1/nx100

All problems of this chapter can be solved through two methods:

1 1)    Unitary method

2 2)      Percentage efficiency

Problems:

1.     1) A can do a job in 12 days and B can do the same job in 6 days, in how many days working together they can complete the job?

Solution:

A’s 1 days work = 1/12

B’s 1 days work = 1/6

Therefore (A+B)’s 1 day works = 1/12 +1/6 = 3/2 =1/4

Time taken by both to finish the whole work = 1/1/4 = 4 days

Alternatively:

 Efficiency of A = 100/12 = 8.33%

Efficiency of B = 100/6 = 16.66%

Both A+B = 25%

Time taken by both to finish the whole work = 100/25 = 4 days

2.    2) A can do a job in 10 days, B can do the same job in 12 days and C can do the same job in 15 days. In how many days they will finish the work together?

Solution:

A’s 1 days work = 1/10

B’s 1 days work = 1/12

C’s 1 days work = 1/15

(A+B+C)’s 1 days work = 1/10+1/12+1/15 = 15/60 = ¼

Since they can complete 1/4work in 1 day. So they will finish the whole work in 1/1/4 = 4 days

Alternatively:

A’ efficiency = 10%

B’s efficiency = 8.33%

C’s efficiency = 6.66%

Combined A,B and C = 10+8.33+6.66 = 25%

 Hence they will take 100/25 = 4 days