CAT Work on alternate days - Practice Questions & MCQ

Definition: This concept entails understanding how tasks get completed when individuals or machines perform work, not consecutively, but on every alternate day. This can introduce complexity into time and work problems as the rate of work completion is not uniform daily.

Solved Examples:

A can complete a task in 6 days, while B can complete the same task in 9 days. If they start working together but only on alternate days, with A starting on the first day, in how many days will the task be completed?

Solution:

1. Identify the Total Work (Using Concept 1): LCM of 6 and 9 is 18. So, let’s assume the total work is 18 units.

2. Determine 1 Day Work (Using Concept 2):

- A’s 1-day work = 18 units / 6 days = 3 units/day

- B’s 1-day work = 18 units / 9 days = 2 units/day

3. Combined Work for Two Days:

In the first two days, A will work on day 1 and B on day 2. 

Total work done in 2 days = A's 1-day work + B's 1-day work = 3 units + 2 units = 5 units.

4. Calculate the Number of Cycles and Remaining Work:

As 18 units need to be completed and they complete 5 units in 2 days, in 6 days they will complete 15 units (3 cycles of the 2-day work). 

Remaining work = 18 units - 15 units = 3 units

As A starts the next cycle, A will finish the remaining 3 units on the next day.

5. Total Time:

6 days (from the 3 cycles) + 1 day (A completing the task) = 7 days.

Tips and Tricks:

1. Use Blocks of Days: Instead of calculating for each day, group days in blocks (like the 2-day block in the example) to make calculations easier.

2. Keep Track of Sequence: Always remember who starts first as it can impact the final calculations, especially when there's a remainder of work.

3. Utilise Previous Concepts: Concept of total work and 1-day work are foundational. Use them to derive the efficiencies of workers before jumping into alternate day calculations.

Application of Previous Concepts:

- Quantify Total Work Using Concept 1: The first step was to determine the total work using the LCM method.

- Determine Daily Efficiency Using Concept 2: After quantifying the total work, we determined how much work each individual completes daily.

- Relate to Alternate Days: Then, using the efficiencies, we calculated how much work is done in the set period (2 days in the example) when they work alternately.