Hari Ram works alone for 8 days on a job and finds that only one-third of the total work has been completed. He then employs Satya, who is 60% as efficient as Hari Ram. If Satya alone has to complete the remaining work, for how many additional days will he need to work?

Introduction / Context:
This problem combines the idea of partial work completed by one person and the remaining work completed by another person with a different efficiency. It tests your ability to translate verbal information about fractions of work and relative efficiencies into algebraic equations. The question specifically asks for the extra time taken by the second worker, Satya, working alone to complete the remaining part of the job.

Given Data / Assumptions:

• Hari Ram works alone for 8 days.
• After 8 days, exactly one-third of the total work is completed.
• Satya is 60 percent as efficient as Hari Ram.
• Satya then works alone on the remaining work.
• We must find how many additional days Satya needs to finish the job.

Concept / Approach:
First, we deduce Hari Ram's daily work rate from the information that he completes one-third of the work in 8 days. Then we use the given efficiency comparison to find Satya's daily work rate. The remaining work is two-thirds of the total. Dividing this remaining work by Satya's rate gives the time he will take alone. Mixed numbers will appear naturally in this calculation, so they must be converted and simplified carefully.

Step-by-Step Solution:
Let the total work be 1 unit. Hari Ram completes 1 / 3 of the work in 8 days. So Hari Ram's daily work rate = (1 / 3) / 8 = 1 / 24 of the work per day. Satya is 60 percent as efficient as Hari Ram. So Satya's daily work rate = 60 percent * (1 / 24) = (60 / 100) * (1 / 24) = 3 / 5 * 1 / 24 = 1 / 40 of the work per day. Remaining work after Hari Ram's 8 days = 1 − 1 / 3 = 2 / 3 of the work. Let T be the number of days Satya needs to finish this remainder. Then T * (1 / 40) = 2 / 3. So T = (2 / 3) * 40 = 80 / 3 days. Convert 80 / 3 to a mixed number: 80 / 3 = 26 2 / 3 days.

Verification / Alternative check:
You can check by recombining both parts. Hari Ram's 8 days produce 8 * (1 / 24) = 1 / 3 of the work. Satya's 26 2 / 3 days produce (80 / 3) * (1 / 40) = 80 / 120 = 2 / 3 of the work. Total work = 1 / 3 + 2 / 3 = 1 unit, confirming that the entire job is completed.

Why Other Options Are Wrong:
Values like 24 1/2 or 24 2/3 days correspond to solving with an incorrect rate for Satya or miscomputing the remaining work fraction. 25 3/2 days is also an incorrect simplification of the fraction 80 / 3. Only 26 2/3 days satisfies the exact equation T / 40 = 2 / 3.

Common Pitfalls:
A common error is to interpret “60 percent as efficient” as meaning Satya completes 60 percent of the job in the same time that Hari Ram completes 100 percent, but then miscalculate the resulting rate. Another pitfall is to treat one-third as 0.3 instead of 1 / 3, which introduces rounding errors and wrong answers. Always work with exact fractions in such problems.

Final Answer:
Satya alone will need 26 2/3 days to complete the remaining work.