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Work and Time Problem-Solving Concept:

1. Work and Time

In work and time-related problems, the concept is based on the relationship between work done, time taken, and the efficiency of the workers. The key points to consider are:

1. Work: This refers to the total amount of work that needs to be completed, usually expressed as 1 (a complete job).

2. Time: The time taken to complete the work by one or more workers. Time is typically expressed in days, hours, etc.

3. Efficiency: The amount of work done per unit of time (e.g., per day). If a person can complete a job in 'n' days, their efficiency or rate of work is 1/n (i.e., they complete 1/n of the work in one day).

4. Combined Work: If two or more workers are working together, their combined work rate is the sum of their individual work rates. For example, if Worker A completes 1/10 of a job in 1 day and Worker B completes 1/20 of a job in 1 day, their combined work rate will be (1/10) + (1/20) = 3/20 of the job per day.

5. Formula: The formula used for solving work and time problems is generally:
Work Done = Rate of Work × Time
Time = Work Done / Rate of Work

6. Solving Together: When two or more people work together, their total efficiency is added together. For example, if A takes 10 days to complete the work and B takes 15 days, then together they will complete the job in less time:
Work done by A in 1 day = 1/10
Work done by B in 1 day = 1/15
Combined work done in 1 day = (1/10) + (1/15)
Solve for the total time they will take together to finish the work.

7. Inverse Relationship: The relationship between time and efficiency is inversely proportional. If the efficiency of a worker increases, the time taken decreases, and vice versa.

1. A alone can do a job in 40 days. In how many days can B alone do the job, if together they can do the job in 8 days?

A)5 days

B)10 days

C)15 days

D)20 days

2. A does work in 15 days and B does the same work in 20 days. In how many days they together will do the same work?

A) 5.0 days

B) 5.8 days

C) 8.57 days

D) 10 days

3. A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. How long would A take separately to do the same work?

A) 5.0 days

B) 10 days

C) 20 days

D) 30 days

4. 30 men are engaged to a work by a contractor for 6 days. They work for 4 days but due to some reasons, only 50% of the work will be completed. How many more men should be engaged to work to complete the work in a given period of time.

A) 5 men

B) 10 men

C) 20 men

D) 30 men