Question

It takes $8$ days for $12$ men to construct a wall. How many men should be put on the job if it is required to be constructed in $6$ days?

Answer 1

Hint: In this question we have been provided with the data that it takes $8$ days day for $12$ men to construct a wall. We will solve this question by first finding the time it will take for a single man to construct the wall. We will then divide the time it takes for one man to complete by $6$, to get the number of men required to construct the wall in $6$ days.

Complete step-by-step answer:
We know that It takes $8$ days for $12$ men to construct a wall and we have to find the time it takes for $6$ men to construct the wall. Mathematically we can write:
Time taken by $12$ men to construct a wall $=8$ days.
Therefore, the time taken by $1$ man will be the number of days multiplied by the number of men. Mathematically we can write:
Time taken by $1$ man to construct a wall $=12\times 8$ days.
Now since we know the time it takes for $1$ man to construct the wall, we will divide the number of days by $6$ to get the number of days it takes for $6$ men to construct the wall. Therefore, we have:
Time taken by $6$ men to construct a wall $=\dfrac{12\times 8}{6}$ days.
On simplifying, we get:
Time taken by $6$ men to construct a wall $=16$ days. Which is the required solution.

Note: In this type of questions, it is to be remembered that when it takes a certain number of days to complete a task, when the number of men is greater, then the number of days it takes will be lesser and when the number of men is less, then the day it takes to complete the task will be greater.