**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:

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

- Speed is in direct variation with work. That means, if speed increases, rate of work also increases.
- Distance is in direct variation with work. That means, to cover more distance, more work has to be done.
- 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

DD