Question

If 12 men can do a piece of work in 18 days, in how many days 8 men will complete this work?
$
  {\text{A}}{\text{. 12}} \\
  {\text{B}}{\text{. 2}}7 \\
  {\text{C}}{\text{. 10}} \\
  {\text{D}}{\text{. }}\dfrac{{{\text{16}}}}{3} \\
 $

Answer 1

Hint- Here, we will proceed by finding the amount of the work completed (in man-days) by 12 men in 18 days and then, we will equate this work done with the work completed when only 8 men will be employed.

Complete Step-by-Step solution:
Given, 12 men can do a piece of work in 18 days
Let x be the number of days in which 8 men will complete the same amount of work
As we know that
Amount of work = (Number of men)$ \times $(Number of days taken)
Amount of work in the first case where the number of men is 12 men and the number of days taken is 18 days
Amount of work in the first case = (12 men)$ \times $(18 days) = (12$ \times $18) man-days = 216 man-days
Amount of work in the second case where the number of men is 8 men and the number of days taken is assume to be x days
Amount of work in the second case = (8 men)$ \times $(x days) = (8$ \times $x) man-days = 8x man-days
Since, the amount of the work which needs to be finished remains same in both the cases
i.e., Amount of work in the first case = Amount of work in the second case
$ \Rightarrow $216 man-days = 8x man-days
$ \Rightarrow x = \dfrac{{216}}{8} = 27$ days
Therefore, a total 27 days will be taken by 8 men to complete the same work as done by 12 men in 18 days.
Hence, option B is correct.

Note- In these types of problems, the amount of the work done remains constant irrespective of the number of men employed or number of days taken i.e., (Number of men)$ \times $(Number of days taken) = constant (usually). It is important to make sure that the units should be the same of the similar quantities taken in the formula.