$10$ men working $6$ hours a day, can complete a work in $18$ days. How many hours a day must $15$ men work, to complete the same work in $12$ days?
A) $4$
B) $5$
C) $6$
D) $7$

Hint: Always convert the time taken all together by the people working along with the count of the people and the number of hours taken and then frame the equation according to the work to be done by the desired number of people and the days of working. Place the values and simplify for the required resultant value.

Complete step by step solution:
Given that: $10$men working $6$hours a day, can complete a work in $18$days
Can be expressed as:
In $18$days, man work $ = 6 \times 10$hours $ = 60$hours
If work is done to complete in one day $ = 6 \times 10 \times 18$hours
To complete the same work in one day by $15$men $ = \dfrac{{6 \times 10 \times 18}}{{15}}$hours a day
Now, the same work done in $12$ days by $15$men $ = \dfrac{{6 \times 10 \times 18}}{{12 \times 15}}$hours a day
Simplify the above expression, removing common factors from the numerator and the denominator.
Work done in $12$ days by $15$men $ = 6$hours a day

Therefore, $15$ men working $6$ hours a day, can complete the work in $12$ days. So, option (C) is the correct answer.

Note:
Understand the data given in the question clearly, then frame the equations accordingly and simplify the expressions accordingly. Always convert the total time required to complete the work by the given number of men. Then convert the time taken by the desired number of men. Be good in division and multiples and remember that the common factor from the numerator and the denominator cancels each other.