CAT Concept of total work - Practice Questions & MCQ

Definition: Total work refers to the complete task or job that needs to be accomplished. In questions related to time and work, it’s crucial to understand the entire scope of the work because all further calculations, be it regarding time or the number of workers required, will revolve around this concept.

Solved Examples

If A can complete a work in 5 days and B in 10 days, how long will they take to complete the    work together?

Solution:

1. Find the Total Work: Instead of taking the work as abstract, let's quantify it. A common method is to take the LCM (Least Common Multiple) of the days taken by the workers. LCM of 5 and 10 is 10.

Thus, let's assume the total work is 10 units.

2. Find Work Done Per Day:

- A completes the work in 5 days, so A's 1-day work = 10 units / 5 days = 2 units/day

- B completes the work in 10 days, so B's 1-day work = 10 units / 10 days = 1 unit/day

3. Combined Work:

If A and B work together, in a day they will complete = A's 1-day work + B's 1-day work

= 2 units + 1 unit = 3 units/day

4. Time to Complete Together:

Total work / Combined 1-day work = 10 units / 3 units/day = 3⅓ days or 3 days and 1/3 of a day.

Tips and Tricks:

1. Quantify the Work: Always start by quantifying the total work. This makes it easier to understand and calculate further. The LCM method is highly effective in doing so.

2. Uniform Work: Assume the work is uniform across days unless stated otherwise. For example, if A can complete a job in 5 days, it means A does 1/5 of the job each day.

3. Break it Down: Breaking down the total work into daily tasks can provide clarity on the progress and help in identifying bottlenecks or efficiencies.

To truly master this concept, it’s imperative to practise with multiple questions from previous years. This helps in understanding the varied ways in which questions can be framed and the nuances that can be introduced in the problems.