Twenty-two men can complete a job in 16 days (constant rate). In how many days will thirty-two men complete the same job?

Introduction:
With constant efficiency and identical workers, total work in man-days remains fixed. Increasing the number of men reduces the number of days in inverse proportion. Here, the computed answer does not appear among the numeric choices, so “None of these” is the correct selection.

Given Data / Assumptions:

• Total work W = 22 men * 16 days.
• New headcount = 32 men.
• All workers retain identical, constant productivity.

Concept / Approach:
Compute W and divide by 32 to get the new time D. If D does not match an option, choose “None of these.” This ensures consistency with the precise arithmetic rather than forcing a rounded or incorrect choice.

Step-by-Step Solution:

Verification / Alternative check:
Ratio method: days scale by 22/32 when men increase to 32: D = 16 * (22/32) = 16 * 0.6875 = 11 days, same result.

Why Other Options Are Wrong:
14, 12, 16, 10 do not equal 11 and hence are incorrect. Therefore “None of these” is appropriate.

Common Pitfalls:
Rounding to the nearest listed value. In standardized tests, exact arithmetic governs; pick “None of these” when the computed exact value is absent.

Final Answer:
None of these