Time and Work Relation between efficiency and time

Relation between efficiency and time

Efficiency is inversely proportional to the time (i.e., number of days, hours, minutes) etc.

Problems:

1.      A takes 16 days to finish a job alone, while B take 8 days to finish the same job. What is the ratio of their efficiency and who is less efficient.

Solution:

Since A takes more time than B to finish the same job hence A is less efficient or

Efficiency A = 100/16 = 6.25%

Efficiency B = 100/8 = 12.5 %

Ratio of efficiency of A:B = 1/16: 1/8 = 1:2

Hence, B is twice efficiency as A.

2.      A is thrice efficient as B and A takes 20 days to do a job, then in how many days B can finish the same job?

Solution:

Ratio of efficiency of A:B = 3:1

Therefore ratio of required days of A:B = 1/3:1/1 = 1:3

Now since A takes 20 days. So B will take 60 days to finish the same job.

3.      P is thrice as efficient as Q and is therefore able to finish a piece of work in 60 days less than Q. Find the time in which P and Q can complete the work individually.

Solution:

Efficiency of P:Q = 3:1

Required number of days of P:Q = 1:3

I.e., if P requires X days then Q requires 3x days

But      3X-X = 60

            2X = 60

            X=30   and 3X = 90

Thus P can finish the work in 30 days and Q can finish the work in 90 days.

4.      A is twice as good a workman as B and is therefore able to finish a piece of work  in 30 days less than B. In how many days they can complete the whole work; working together?

Solution:

Ratio of efficiency = 2:1 (A:B)

Ratio of required time = 1:2(A:B) = X:2X

But
 = 2X-X =30

X=30  and 2X=60

Now Efficiency of A = 3.33%

And Efficiency of B = 1.66%

Combined efficiency of A and B together = 5%

Therefore time required by A and B working together to finish the work

= 100/5 = 20 days

Note:

Efficiency = 1/number of time units

Efficiency x time = constant work

Hence required time = work / efficiency

Whole work is always considered as 1, in terms of fraction and 100%, in terms of percentage.

In general, number of days of hours = 100/efficiency