Nirmit can complete two-thirds of a job in 18 days. Kashish is twice as efficient as Nirmit. In how many days will Kashish alone complete the entire job?

Introduction / Context:
This question compares the efficiencies of two workers, Nirmit and Kashish. We are told how long it takes Nirmit to complete a fraction of a job and that Kashish is twice as efficient as Nirmit. Based on this, we must determine how long Kashish would take to complete the full job alone. Questions of this type test the understanding of work rates and the effect of relative efficiency on completion time.

Given Data / Assumptions:

• Nirmit completes two-thirds (2/3) of a job in 18 days.
• Kashish is twice as efficient as Nirmit.
• We must find the time Kashish alone needs to complete the entire job.
• Total work is taken as 1 full job.
• Efficiencies and work rates remain constant.

Concept / Approach:
First we calculate Nirmit daily work rate using the information about two-thirds of the job completed in 18 days. Once we know Nirmit rate, we find Kashish rate by doubling that value since Kashish is twice as efficient. To find how long Kashish alone takes to complete the entire job, we divide the total work, which is 1 job, by Kashish daily rate. This method is straightforward and relies on careful handling of fractions.

Step-by-Step Solution:
Step 1: Let total work be 1 job. Step 2: Nirmit completes 2/3 of the job in 18 days. Step 3: Nirmit daily rate = (2/3) / 18. Step 4: Simplify: (2/3) / 18 = (2/3) * (1/18) = 2 / 54 = 1/27 job per day. Step 5: Kashish is twice as efficient as Nirmit, so Kashish daily rate = 2 * (1/27) = 2/27 job per day. Step 6: Time taken by Kashish alone to complete 1 job = 1 / (2/27). Step 7: Simplify: 1 / (2/27) = 27/2 days. Step 8: Therefore, Kashish will complete the job in 27/2 days, which is 13.5 days.

Verification / Alternative check:
To check, in 13.5 days Kashish at rate 2/27 job per day completes 13.5 * (2/27) jobs. Converting 13.5 to a fraction gives 27/2. So work done = (27/2) * (2/27) = 1 job. This confirms that 27/2 days is exactly correct. Moreover, Nirmit rate being half of Kashish rate means Nirmit would take 27 days to complete the job, which is consistent with him taking 18 days to complete two-thirds of it.

Why Other Options Are Wrong:
Values such as 29/4 days, 31/2 days, or 13/2 days correspond to different daily rates and do not satisfy the condition that Kashish is exactly twice as efficient as Nirmit. Likewise, 15 days would yield a smaller daily rate for Kashish, which would not match the given efficiency relationship. Only 27/2 days keeps all the relationships consistent and correctly matches the calculated rates.

Common Pitfalls:
A common mistake is to assume that if Nirmit takes 18 days for 2/3 of the work, then he takes 18 days for the remaining 1/3 as well, which is not directly used here. Instead, we must convert to a daily rate first. Another error is forgetting to double the rate and instead halving the time without verifying. Always convert efficiency statements into precise rate relationships and then compute time from those rates.

Final Answer:
Kashish alone will complete the entire job in 27/2 days.