Time and Work - Important Points
Questions related to time and work are asked in many competitive exams. Let's understand its concepts and tricks.
Time and Work Tricks
Tricks to solve time and work problems lies in its approach.
Concept of per day work
If A can do a job independently in 10 days, then in 1 day he does 1/10 th of the job.
Similarly if a person can do 1/x part of a work in 1 day, he will complete the full work (whole part) in 1/(1/x) = x days.
Example 1: A completes a work alone in 10 days, B complete in 12 days while C completes it in 15 days. Working together, in how many days, they can complete the work?
Solution:
Work/Day
A 1/10
B 1/12
C 1/15
In 1 day they all together completes (1/10 + 1/12 + 1/15) = 15/60 work
So, the work can be completed in = 1/(15/60) = 4 days
Note: In the above solution, we have observed fractions which is due to taking the whole work as 1 unit. It can be avoided by taking total work as the LCM of their individual days.
Time and Work LCM Method
Using the LCM method in time and work questions, calculation time can be reduced significantly.
Let’s take the Example 1 to illustrate LCM method-
Total work = LCM (10, 12, 15) = 60
Work/Day
A 6
B 5
C 4
In 1 day, they all together completes (6 + 5 + 4) = 15 unit work
So, the whole work will be completed in = 60/15 = 4 days
Time and Work type wise Questions
A. All working together
B. Someone joins/left after some days
C. Working on alternate days
D. Distribution of wages
E. Working on different efficiencies
Let’s take an example to illustrate the above types-
Example 2: A completes a work alone in 10 days, B complete in 15 days while C completes it in 30 days. Find -
(a) In how many days the work will be completed if all working together
(b) All worked together for 4 days then A and B left. In how many days remaining work will be completed by C alone.
(c) All worked together for 3 days and then A left. In how many days the remaining work will be completed if B and C working on alternate days.
(d) If they all worked together and complete the work, what will be share of C if Rs. 600 is allotted for the whole job.
(e) In how many days the work will be completed if B works with half of his efficiency whereas C works on his double his efficiency.
Solution:
Total work = LCM (10, 15, 30) = 30
Work/Day
A 3
B 2
C 1
(a) In 1 day, they all together completes (3 + 2 + 1) = 6 unit work
So, the whole work will be completed in = 30/6 = 5 days
(b) Work done in 4 days = 4 x 6 = 24
Work remaining = 30 – 24 = 6
Time taken by C to complete it = 6/1 = 6 days
(c) Work done in 3 days = 3 x 6 = 18
Work remaining = 30 – 18 = 12
Working on alternate days, B and C can do 2 + 1 = 3 unit of work in 2 days
Time taken by then to complete it = (12/3) x 2 = 8 days
(d) The wages will be distributed in the ratio of their efficiencies (work/day).
C’s share = (1/6) x 600 = Rs. 100
(e) B works with half of his efficiency, then he does 1 unit/day whereas C works on his double his efficiency, so, he does 2 units/day.
In 1 day, they all together completes (3 + 1 + 2) = 6 unit work
So, the whole work will be completed in = 30/6 = 5 days
Concept of Man days
If M = number of men
D = number of days in which work is completed
H = number of hours per day each men working
W = amount of work
Then, W = MDH = Constant
Example 3: 10 men working 8 hrs a day completes a job in 5 days. Then in how many days-
(a) 20 men working 5 hrs a day complete the job.
(b) If 5 men worked 8 hrs a day for 5 days then in how many more men are required to complete the remaining job in just 1 day (each men working 8 hrs a day).
Solution: W = 10 x 8 x 5 = 400
(a) 400 = 20 x 5 x d
=> d = 4 days
(b) Work done = 5 x 8 x 5 = 200
Work remaining = 400 – 200 = 200
200 = 8 x 1 x m
=> m = 25
=> 25 – 5 = 20 more men are required.