Question

If \[5\] men can build a wall in \[12\] days. How many men can build it in \[10\] days?
A. \[6\]
B. \[7\]
C. \[8\]
D. \[4\]

Answer 1

Hint: We are asked to find the number of men required to build a wall in \[10\] days. We are given information of how many men needed to build the same wall in \[12\] days. Use this information to find the total work needed to build the wall. Total amount of work for \[10\] days and \[12\] days will be the same, use this concept to find the required number of men.

Complete step-by-step answer:
Given, \[5\] men can build a wall in \[12\] days
We are asked to find the number of men needed to build the wall in \[10\] days.
Let \[x\] men can build the wall in \[10\] days.
Let \[w\] be the work done by one man in one day
Let \[W\] be the total work done to build the wall.
If \[w\] is the work done by one man in one day, then work done by \[5\] men in one day will be \[ = 5 \times w\]
 \[5\] men does \[5 \times w\] amount of work in one day, in \[12\] days amount of work done by \[5\] men will be \[ = 5 \times w \times 12\]
And it is given that in \[12\] days, \[5\] men can build the wall. Therefore work done by \[5\] men in \[12\] days will be equal to the total work. So, we can write
 \[5 \times w \times 12 = W\] (i)
Similarly, the amount of work done by \[x\] men in one day will be \[x \times w\] and in \[10\] days, the amount of work done by \[x\] men will be \[ = x \times w \times 10\] , which will be equal to the total work. So, we can write
 \[x \times w \times 10 = W\] (ii)
Now, equating equations (i) and (ii), we get
 \[5 \times w \times 12 = x \times w \times 10\]
 \[ \Rightarrow 5 \times 12 = x \times 10\]
 \[ \Rightarrow x = \dfrac{{5 \times 12}}{{10}}\]
 \[ \Rightarrow x = \dfrac{{60}}{{10}}\]
 \[ \Rightarrow x = 6\,{\text{men}}\]
Therefore, the number of men required to build the wall in \[10\] days is \[6\,{\text{men}}\] .
So, the correct answer is “6 Men”.

Note: For such types of problems, where work is involved, remember that total work to be done will be the same and it will not depend on the number of days or men. So, using this concept we can form equations to find the desired answer. And also, check for the extra information given in the question to form equations.