Basics of Time and Work
In this article we will understand the basics of Time and Work.
Assumptions in Time and Work
There are some basic assumptions that are made while solving Time and Work problems.
Work to be done is usually considered as one unit.
Every person does the work uniformly, i.e., until and unless specified explicitly, any given person is supposed to do the same amount of work everyday.
In a team people share the work equally.
Similarity with TSD
Problems based on Work and Time are very similar to problems on Time, Speed and Distance.
- Rate of doing work or Efficiency is similar to Speed
- Amount of work done is similar to the Distance travelled.
- Time taken to complete a work is similar to Time taken to travel a distance.
So, Time taken to complete a work = Amount of work / Efficiency
(Just as, Time taken to cover a distance = Distance / Speed)
Let us now try to understand the concept of efficiency in much more detail.
Concept of Efficiency
If number of days required to complete the task (i.e. time-taken) = x
Then person’s 1 day work, i.e. Efficiency (or work-rate), n = 1/x
Or, we can look at it this way:
Number of days required to complete the task, x = Total Work/Work done in one day = Total Work/Efficiency = 1/Efficiency = 1/n
Note: In general we do not know the total amount of work. So, we assume Total Work = 1 (always, unless otherwise specified)
Though later we will learn how to assume total amount of work as some LCM to avoid the fractions in calculation.
So, Efficiency (or work-rate) = 1/Time-taken
OR
Number of days required to complete the task, i.e. Time-taken = 1/Efficiency
Either way:
Time taken α 1/Efficiency
Q. A, B and C can do a piece of work in 3, 4 and 5 days respectively. They completed a work together and received Rs. 470. What is B’s share?
Explanation:
And the amount of work done by them will be in proportion to the amount of work done by them per day (i.e. their efficiency), as all of them work for the same number of days.
So, ratio of their efficiencies = 1/3 : 1/4 : 1/5 = 20 : 15 : 12
Hence, B’s share = (15/47) × 470 = Rs. 150
Time – Work Equivalence
Work done = Number of men × Number of days × Number of hours per day
Or W = M × D × H
If $M_1$ persons can do $W_1$ work in $D_1$ days for $H_1$ hours and $M_2$ persons can do $W_2$ work in $D_2$ days for $H_2$ hours, then
$\frac{M_1 D_1 H_1}{W_1}$ = $\frac{M_2 D_2 H_2}{W_2}$
Concept of man-days
Man-days: The number of men multiplied by the number of days that they take to complete the work.
The total number of man-days required to complete a specific task is a constant. That is, the product of the two variables, men and days, is a constant.
So, number of men and number of days are inversely proportional to each other, when work is constant.