Time and Work Concepts

Understanding the Concepts of Time and Work

Time and work problems develop when a given quantity of work must be completed in a specific length of time. There are different types of problems.

• Group efficiency problems

• Individual efficiency problems with people

Individual efficiency problems with pipes and cistern, with the notion of negative work included

For the benefit of cross-material learnings, we shall use the phrase Time & Work to refer to individual efficiency problems with people from now on.

These sorts of problems can be addressed utilising two approaches:

1. Fraction method or Unitary work Method
2. LCM Method

To have a better understanding of these concepts, let's look at an example and solve both of the following:

1. Fraction Method or Unitary Work Method

In this method we will assume the total work to be 1 unit and calculate the individual efficiency in terms of fractions and solve the problem. Let's solve the above example problem by using the fraction method to understand it better.

Example Problem

Person A and B can do a piece of work in20 and 30 days respectively. If both of them work together, in how many days will the work be completed?

Step 1: Assume the total work to be 1.

Step 2: Calculate the individual efficiencies of the given people

Here,Person A will complete the work in 20 days, So in 1 day he will do 1/20th of the total work.

Person B will complete the work in 30 days, So in 1 day he will do 1/30th of the total work.

Step 3: Calculate the combined efficiency of both these people in a day

Here, Combined work done in 1 day = ((1/20) + (1/30))

After solving we get,Combined work done in 1 day = 1/12

Step 4: Taking the inverse of work done in 1 day will give us the total time taken to complete the task.

So, If both of them work together, work will be completed in 12 days.

2. LCM Method

In this method we will assume the total work to be the LCM of the given numbers and calculate the individual efficiency in terms of integers and solve the problem. This will help us to solve the problem faster. Let's solve the above example problem by using the fraction method to understand it better.

Example Problem

Person A and B can do a piece of work in20 and 30 days respectively. If both of them work together, in how many days the work will be completed?

Step 1: Assume the total work to be LCM of 20 and 30, Here LCM = 60.

Step 2: Calculate the individual efficiencies of the given pipes with LCM as total work.

Here,

• Person A will do the entire work (60 work) in 20 days , So in 1 day it will fill 60/20 of the tank= 3 work/day.
• Person B will do the entire work (60 work) in 30 days , So in 1 day it will fill 60/30 of the tank= 2 work/day.

Step 3: Calculate the combined efficiency of both the persons in a day

Here,

• Combined work done in 1 day = 3+2 Solving these we get ,
• Combined work done in 1 day = 5 work / day

Step 4: Divide the total work by the work done in 1 day ⇒ 60/5 ⇒ 12 days.

So, If both of them work together, work will be completed in 12 days.

There can be several types of questions asked in Time and Work, and essentially all of them can be addressed by utilizing the aforementioned methods.