Arun works alone for 8 days and finds that only one third of the work has been completed. He then employs Akhil, who is 60 percent as efficient as Arun, and allows Akhil to complete the remaining work alone. How many more days will Akhil take to finish the remaining two thirds of the work?

Introduction / Context:
This question involves changing workers in the middle of a job and comparing their efficiencies. Arun starts the work and later Akhil, who is less efficient, completes what is left. Many aptitude tests include such problems to check understanding of fractional work and relative efficiencies. The task is to quantify the rate at which Arun works, use it to compute Akhil's slower rate, and then determine how long Akhil alone will need to finish the remaining work.

Given Data / Assumptions:

• Arun works alone for 8 days and completes one third of the work.
• Akhil is 60 percent as efficient as Arun.
• After the first 8 days, only Akhil works on the remaining part of the job.
• We assume both Arun and Akhil work at constant daily rates.
• We are asked to find how many more days Akhil alone will take to complete the remaining two thirds of the work.

Concept / Approach:
The main concept used is work rate. If a worker completes W fraction of the job in T days, the rate is W / T per day. First we compute Arun's daily work rate from the statement that one third of the work is done in 8 days. Then we use the fact that Akhil is 60 percent as efficient, meaning his rate is 0.6 times Arun's rate. Once we know Akhil's rate, we divide the remaining work, which is two thirds of the job, by this slower rate to get the additional time he needs.

Step-by-Step Solution:
Step 1: Arun completes one third of the work in 8 days, so Arun's rate is (1/3) / 8 = 1 / 24 of the job per day. Step 2: Akhil is 60 percent as efficient as Arun, so Akhil's rate is 0.6 times 1/24, which is 1 / 40 of the job per day. Step 3: Fraction of work remaining after Arun stops is 1 minus 1/3 which equals 2 / 3 of the job. Step 4: Time required by Akhil alone is (2/3) divided by (1/40) which equals (2/3) times 40 = 80 / 3 days. Step 5: 80 / 3 days is approximately 26.666 days, which is written as 26.6 days in the options.

Verification / Alternative check:
If we think of the total work as 120 units, Arun completes 40 units in 8 days, so his rate is 5 units per day. Akhil, at 60 percent of that rate, completes 3 units per day. Remaining work is 80 units. At 3 units per day, Akhil needs 80 / 3 days, which again equals 26.666 days. This confirms the fraction based calculation and shows that the approximate option 26.6 days is correct when rounded to one decimal place.

Why Other Options Are Wrong:

• 24.5 days and 25 days underestimate the time needed since Akhil is slower than Arun and has to complete two thirds of the work.
• 20 days is much too small and would imply a significantly higher work rate for Akhil than given.
• Only 26.6 days correctly represents 80 divided by 3 when rounded to one decimal place.

Common Pitfalls:
Students sometimes mistakenly let Arun and Akhil work together on the remaining work or misinterpret 60 percent efficiency as a time ratio instead of a rate ratio. Another frequent error is to subtract 60 percent from the number of days rather than from the rate. Always remember that efficiency percentages apply to work rate, not directly to the number of days, and that remaining work must be calculated accurately before dividing by the new worker's rate.

Final Answer:
Akhil alone will take approximately 26.6 days to finish the remaining work.