Time and Work Formula

Time and Work is another important section of quantitative aptitude where conceptual clarity of relationship between working efficiency and time is very important to understand.

Time and Work Tricks

Work to be done is generally considered as one unit. It may be digging a trench constructing or painting a wall, filling up or emptying a tank, reservoir or a cistern.

Working Efficiency Concepts

Working Efficiency is the work done by an individual in one day and this efficiency is inversely proportional to the number of days to complete a work. It means that a person who takes less days to complete a work. It means that a person who takes less days to complete a work is said to be more efficient than a man who takes more days to complete the same work.
This relationship can be explained with the help of the following example.
If A can do a piece of work in 20 days and B can do the same work in 10 days, then in how many days the work will be completed if both of them work together.
It is given that A does a work in 20 days hence working efficiency of A is 1/20 work in one day. Similarly working efficiency of B is 1/10 work in one day. Hence combined working efficiency of both of them in one day = ( 1/20 + 1/10 ) = 3/20 work.
In other words, both of them working together will complete 3/20 work in one day.
Therefore, they will complete 1 work in 20/3 days. 

General Rules to be followed in Time and Work Problems

1. If A can do a piece of work in n days, then work done by A is 1/n. i.e, if a person can do some work in 12 days, he does 1/12 of the work in one day.
2. If A's 1 day work = 1/n, then A can finish the whole work in n days, i.e, if a person's one day work is 1/10, then he can finish the whole work in 10 days.
3. If A is thrice as good a workman as B, then ratio of work done by A and B is 3:1, i.e, if a man works three times as fast as a woman does, then when the work is complete 3 parts of the work has been done by the man and 1 part by the woman.
4. If A is thrice as good a workman as B, then ratio of time taken by A and B = 1:3. i.e, if the woman takes 15 days to complete the work, then the man takes 5 days to complete the same work.
5. If two persons A and B can individually do some work in a and b days respectively, then A and B together can complete the same work in ab(a+b) days.
6. The fundamental rules on variation also apply in Time and Work.

  • Work and men are directly proportional to each other, i.e., if the increase in number of men required increases to complete the work in the same number of days and vice-versa.
  • Men and days are inversely proportional, i.e., if the number of men increases, the increases, the number of days required to complete the same work decreases and vice-versa.
  • Work and days are directly proportional, i.e., if the work increases, the number of days required also increases, if the work is to be completed with the same number of men and vice-versa.

Time and Work Management

Money and Health once lost can be recovered to a great extent if not fully; however time and work once lost cannot be recovered under any circumstances. Man is endowed with a limited time in his lifetime. He is the architect of his own time and work management. If he makes a proper division of his time and work which he does his duty accordingly, he is sure to improve and prosper in life. But if he chooses to turn his back upon his duty, he is bound to repent at leisure. Time and work brings opportunities, and the passing time makes them slip out. When the opportune time has passed, man can do nothing but cry over its loss, once again wasting the precious time at his disposal. After all, our life is a sum total of hours and minutes, and wasting it is like committing culpable homicide. Youth is the prime time and prime work of one's life; it is the morning of one's life. It is wasted, it is equal to wasting the morning hours after which the whole day turns into a dull time. If time of youth is wasted, its consequences can be easily imagined. It is the time when one's personality is moulded, so only Carlyle termed this period as the seed time of life. We enjoy the fruits of youth later in life, so we should carefully make optimum use of it.