Question

A can do a job in 24 days and B can do the same job in 26 days. A and B do the work in alterative days. If 'B' starts the work, find in how many days the job got complete

• A. 25
• B. 27
• C. 24
• D. 35
• E. None of these

Answer 1

Answer: (E)

Step 1: Understand the problem.
A can complete the job in 24 days, and B can complete the same job in 26 days. A and B work alternately, with B starting the work. We need to find the total number of days required to complete the job.

Step 2: Calculate the work done by A and B per day.
- A can do the entire job in 24 days, so A's rate of work is \( \frac{1}{24} \) of the job per day.
- B can do the entire job in 26 days, so B's rate of work is \( \frac{1}{26} \) of the job per day.

Step 3: Calculate the total work done in one cycle of alternating work.
In one cycle, A and B work together for two days. The total work done in two days is:
Total work in 2 days = A's work + B's work
Total work in 2 days = \( \frac{1}{24} + \frac{1}{26} \)
To find the total work, we need to calculate the sum: \[ \frac{1}{24} + \frac{1}{26} = \frac{26 + 24}{24 \times 26} = \frac{50}{624} \] So, in two days, \( \frac{50}{624} = \frac{25}{312} \) of the job is completed.

Step 4: Calculate the number of cycles required to complete the job.
To complete the entire job, we need to determine how many cycles (of 2 days) are needed to complete 1 job:
Number of cycles = \( \frac{1}{\frac{25}{312}} = \frac{312}{25} = 12.48 \) cycles.
Since we need a whole number of cycles, we round up to 13 cycles.

Step 5: Calculate the total number of days.
Since each cycle is 2 days, the total number of days required is:
Total days = \( 13 \times 2 = 26 \) days.

Step 6: Conclusion.
The job is completed in 26 days.

Final Answer:
The correct option is (E): None of these.