Time and Work

An individual or a group of individuals may finish a piece of work in the time it takes them and the efficiency with which they do it. This is referred to as time and work.

Here are some questions related to time and work:

• Determine a person’s level of productivity.
• Determine the amount of time it takes a person to do a certain task.
• Determine how long it takes a group of people to accomplish an assignment.
• Determine the amount of time spent working by one person.
• Determine the amount of work completed by a group of people over a specified period of time.

Time And Work Formulas

Here are some general rules and formulas to solve time and work questions: 

• Work Done = t × r, where t is the time taken, and r is the rate of work.
• Rate of Work = 1 / t, where t is the time taken.
• Time Taken = 1 / r, where r is the rate of work.
• If something is completed in x no. of days, how much work was done in one day? 1/x
• Total Work Done = n × e, where n is the number of days and e is efficiency.
• Time and efficiency are inversely proportional. This means that the more the efficiency, the less is the time required to complete a given task and vice versa. 
• If x:y is the ratio of the number of persons required to complete a task, they finish the given task in y:x time.

Solved Examples

• A builder hires A, B, and C to work on one of his projects. It takes them 20, 30, and 60 days, respectively, to complete the project. If B and C help A every third day, how long would it take him to finish the project?

Total work done by A, B, and C in one day = 1/20 + 1/30 + 1/60 = 6/60 = 1/10

Work done alone by A in two days = 1/10 

On the third day, when they help him, the work done will be 1/10 

Therefore, work completed in 3 days = 1/10 + 1/10 = ⅕

So, the work will be completed in 15 days as 1/5 × 5 = 1

• A and B take 6 and 8 days, respectively, to do a task. They take Rs. 2,400 for their work. The work was done in 3 days when C joined them. How much is to be paid to A?

The work done by A and B will ⅙ and ⅛ respectively. Total work done by them in one day = ⅙ + ⅛ = 8 + 6 / 48 = 14/48 = 7/24

So, work done by C in one day = 1/3 – 7/24 = 8-7 / 24 = 1/24

The amount to be shared between them would be 1/6 : 1/8 : 1/24 = 4:3:1

Total amount paid = Rs. 2,400 x ⅛ = 300

• A can do a piece of work in 10 days. B can do the same work in 15 days. A and B work together for 5 days and leave it. C does the rest of the work in 2 days. They will get Rs. 4,500 for the whole task. How will A, B, and C divide the money?

The work that A and B will do in 5 days = 5 x (1/10 + 1/15) = 5 x (3+2/30) = ⅚

So, the work that remains is 1/6.

So, the ratio of their work will be = (A’s work in 5 days) : (B’s work in 5 days) : (C’s work in 2 days) 

= 5/10 : 5/15 : ⅙

= 15/30 : 10/30 : 5/30

= 15 : 10 : 5

= 3 : 2 : 1

So, how much money will each of them get?

A = 3/6 x 4,500 = 2,250

B = 2/6 x 4,500 = 1,500

C = 1/6 x 4,500 = 750

• 6 women and 8 girls can do a task in 10 days. In comparison, 26 women and 48 girls can finish the task in 2 days. How much time will 15 women and 20 girls take to finish the task?

Let the work done by one woman and one girl in a day be x and y, respectively. 

Therefore, 6x + 8y = 1/10 and 26x + 48y = ½

Solving these equations, x = 1/100 and y = 1/200

So, 15 women and 20 girls will do the task in  15/100 + 20/200 = ¼

Thus, 15 women and 20 girls can do the task in 4 days. 

Conclusion

Time and Work questions are often asked in quantitative aptitude portions in the Government tests. Candidates should be familiar with this subject matter before they take their exams. In essence, time and work is the amount of time it takes an individual or a team to finish a task, as well as the effectiveness of the job performed by each member of the team.