Time and Work

The Time and Work topic is essential for banking and SSC exams, and it primarily tests a candidate’s ability to solve problems related to work efficiency, the relationship between time, work done, and the number of workers. Here’s an overview:

Key Concepts:

1. Basic Formula:

Work Done=Rate of Work×Time Taken

Where rate of work is usually expressed in terms of “work per day” or “work per hour.”

1. Efficiency and Work:

Efficiency is defined as the amount of work done in a unit time (e.g., a person can complete a task in 5 days, their efficiency is 1/5).

If two people, A and B, are working together, their combined efficiency will be the sum of their individual efficiencies.

 

1. Work and Time Inverse Relationship:
   If a person can complete a task in ‘n’ days, then in one day, they complete  1/n of the task.

 

1. Multiple Workers:
   If multiple people are working together, their efficiencies add up.
   For example, if A does a task in 5 days and B in 10 days, their combined efficiency will be:

Combined Efficiency= 1/5 + 1/10 = 3/10​

Hence, they will complete 3/10 of the work in a day.

1. Work Done by Groups:
   If A and B work together but alternate days, different combinations are used to calculate the total work done.

Important Problem Types:

1. Work Sharing:
   Problems involving multiple workers completing a task together or individually.
2. Work and Time Efficiency:
   Comparing efficiency of workers and calculating time taken when efficiency changes.
3. Pipes and Cisterns:
   These are essentially time and work problems where filling and draining are seen as work done. Pipes filling are positive work, and those draining are negative work.
4. Alternate Work:
   Cases where people work on alternate days, with each person completing different parts of the task on different days.
5. Working Together and Separately:
   A common problem where workers start together and then leave or join at different points of the task.

Common Formulas:

• Efficiency-Work-Time Relationship:

Time Taken=Total Work/Efficiency

 Combined Efficiency for workers A and B working together:

Combined Work per Day=1/A′sTime+1/B′sTime

 If A does a task in ‘n’ days and B in ‘m’ days, the number of days they’ll take to finish the work together:

nm/n+m

Approach for Banking and SSC:

• Banking Exams: Focus more on the logical application of the concepts with medium complexity.
• SSC Exams: There are more tricky, calculation-heavy questions, often combining different concepts.

Key Concepts:

1. Filling and Draining:
   • Inlet Pipes: These are pipes that fill the tank. The rate at which they fill the tank is considered positive.
   • Outlet Pipes: These are pipes that empty the tank. The rate at which they drain the tank is considered negative.
2. Work Concept:
   Just like Time and Work, here, the work is represented by the task of filling or emptying a cistern. If a pipe fills a cistern in ‘n’ hours, it fills 1/n  of the tank in one hour. If a pipe empties a cistern in ‘m’ hours, it drains 1/m of the tank in one hour.

 

1. Combined Effect of Pipes:
   If two pipes are working together, one filling and the other emptying the tank, their rates will add algebraically. For example:
   • Pipe A fills the tank in 4 hours (Rate = 1/4 ​).
   • Pipe B empties the tank in 6 hours (Rate = −1/6)
   • Combined rate = 1/4−1/6=1/12

Therefore, both pipes together will fill 1/12 ​ of the tank in one hour, and the whole tank will be filled in 12 hours.