Ehsaan is twice as good a worker as Kamal, meaning he is twice as efficient. Together they finish a piece of work in 29 days. If both work at constant rates, in how many days will Kamal alone finish the same work?

Introduction / Context:
This is another efficiency comparison problem similar in style to other "twice as good" questions. We are told that one worker, Ehsaan, is twice as efficient as Kamal and that together they complete a job in 29 days. We must find how long Kamal alone would take to finish the same job. Problems like this reinforce the relationship between efficiency, work rate, and time.

Given Data / Assumptions:

• Ehsaan is twice as efficient as Kamal.
• Ehsaan and Kamal together finish the work in 29 days.
• Both work at constant rates throughout.
• We are asked for Kamal's individual completion time.

Concept / Approach:
Efficiency is directly tied to work rate. If Ehsaan is twice as efficient as Kamal, his daily rate is twice Kamal's rate. Let Kamal's rate be a base variable and set Ehsaan's rate as twice that. The combined rate is the sum of the two and is known from the 29-day completion time. Solving this equation gives Kamal's rate, and taking the reciprocal of that rate gives the time required for Kamal alone to complete the work.

Step-by-Step Solution:
Step 1: Let total work = 1 unit. Step 2: Let Kamal's daily rate = k units per day. Step 3: Ehsaan is twice as efficient, so Ehsaan's rate = 2k units per day. Step 4: Combined rate of Ehsaan and Kamal together = k + 2k = 3k units per day. Step 5: They complete the job in 29 days, so 3k = 1/29. Step 6: Solve for k: k = 1 / (29 × 3) = 1/87. Step 7: Kamal's rate is 1/87 of the work per day, so Kamal alone will need 87 days to complete the work.

Verification / Alternative check:
If Kamal takes 87 days, then Ehsaan, being twice as efficient, would take half that time: 87/2 = 43.5 days. Their combined rate is 1/87 + 1/43.5 = 1/87 + 2/87 = 3/87 = 1/29, which means together they finish in 29 days as stated. This confirms that the computed time of 87 days for Kamal is consistent with the given information.

Why Other Options Are Wrong:
58 days would imply that Kamal is faster than the slower of the pair implied by the efficiency ratio, and it would not produce the correct joint completion time. Values like 70 or 116 days also lead to combined rates that do not match the 29-day completion time for the pair. Only 87 days yields an exact combined rate of 1/29 per day when combined with Ehsaan's rate of 2/87 per day.

Common Pitfalls:
Many learners misread "twice as good" and mistakenly give Ehsaan twice the time instead of twice the speed. Another common mistake is to treat 29 as directly related to Kamal's time without first using the combined rate. The correct method is to work systematically with rates, starting with the base variable for Kamal's rate and using the given combined duration.

Final Answer:
Kamal alone will finish the work in 87 days.