Correct option is C
Given:
p number of men can finish a piece of work in q days.
There are 50% more men, then the work will be finished 12 days earlier.
Concept Used:
Work is inversely proportional to the number of men and the number of days.
Formula Used:
Work = Men × Days
Solution:
Initial work:
Work = p × q
With 50% more men:
Number of men = p + 0.5p = 1.5p
New days = q - 12
Since the work done is the same:
p × q = 1.5p × (q - 12)
Cancel out p from both sides:
q = 1.5(q - 12)
Expand and solve for q:
=> q = 1.5q - 18
=> q - 1.5q = -18
=> -0.5q = -18
=> q = -18 / -0.5
=> q = 36
∴ The value of q is 36.
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