 ##### What will you learn in this chapter?
• Relationship between Time and Work w.r.t workforce
• The analogy between time, work, distance, and speed
• Efficiency and Rate of filling
##### Exam Connect

Time and Work is a very small and basic chapter but is frequently asked in competitive exams. This chapter is mainly formulae and relationship-based. Understanding and memorizing these will help you bag some extra marks in your competitive exam.

### Time and Work

#### Relationship between Time and Work w.r.t workforce

Relationship between Time and Work is always defined w.r.t workforce. This relationship can be given in two ways:

1. If the work force is more for a certain work, then it will take less time to complete that work.
2. If the work force is less for a certain work, then it will take more time to complete that work.

Let’s understand this relationship with an example. Suppose the work is to build a wall of 6 foot. If there are 4 men doing this work, then it will take more days to complete say 12 days. Similarly, if there are 8 men doing this work, then it will take less days to complete say 6 days. So from this, we can numerically derive that work force is in indirect variation with time for a particular work. That is, if number of men increases, time decreases and if number of men decreases, time increases.

#### Analogy between Time, Work, Distance and Speed

We can derive three relationships between time, work, distance, and speed. Majority of the time these relations are given w.r.t work. So let’s go through it.

1. Speed is in direct variation with work. That means, if speed increases, rate of work also increases.
2. Distance is in direct variation with work. That means, to cover more distance, more work has to be done.
3. Time is in direct variation with work. That means, provided that the workforce is constant, if the amount of work increases, the amount of time required also increases.

#### Efficiency and Rate of Filling

Efficiency can simply be defined as the amount of work a person can do in one day. Always remember that efficiency is inversely proportional to time taken i.e. Efficiency ∝ 1/Time Taken. Efficiency is always given in percentage.

The formula for finding efficiency is (100/n) %, where ‘n’ is the time required.

##### Types of efficiency

Efficiency is mainly of two types. They are:

• Positive efficiency: When efficiency is taken out for work that is done in a constructive way, it is known as Positive Efficiency. For example, if a man builds a wall in 2 days, then the efficiency will be 100/2 = 50%. Here, since building a wall is a constructive work, the efficiency is positive.
• Negative efficiency: When efficiency is taken out for work that is done in a destructive way, it is known as Negative Efficiency. For example, if a man demolishes a wall in 5 days, then the efficiency will be 100/5 = 20%. Here, since demolishing a wall is a destructive work, the efficiency is negative.
##### Net Efficiency

Net efficiency is defined as the difference between positive efficiency and negative efficiency. For example, if the positive efficiency of a man is 50% and the negative efficiency of a man is 20%, then the net efficiency is 50 – 20 = 30%.

Net Efficiency = Positive Efficiency – Negative Efficiency

Now, when it comes to work w.r.t rate, then the number of units of work done per unit time is called the rate of work. So, Work = Rate × Time. To derive this, we can look at the concept, Rate of filling 1/Time Taken.

Rate ∝ 1/Time Taken

Rate = 1/Time Taken

Since, work is denoted as 1

Work = Rate × Time 