Question

$15$ men build a $16.25m$ long wall up to a certain height in one day. How many days’ men should be employed to build a wall of the same height but of length $26m$ in one day?

Answer 1

Hint: This is a simple sum which can be solved by applying a unitary method.
Firstly, we have to find out how long the wall is built by $1$ man and then assume the required number of men is $x$. Finally we get the answer.

Complete step-by-step answer:
It is stated in the question that $15$ men build $16.25m$ long wall in one day.
Here we need to apply unitary method to find out,
Work done by $1$ man in $1$ day where we have to divide the total length of the wall by the total number of men.
Therefore we can write that if $15$ men can do $16.25m$ long wall in $1$ day.
Then, $1$ man can do $\dfrac{{16.25}}{{15}} = \dfrac{{13}}{{12}} m$ length of wall in $1$day.
Now, let us consider $x$ to be the required number of men to be employed to build a wall of length of $26m$.
Now we can say that since $1$ man can do $\dfrac{{13}}{{12}}$ length of wall therefore $\dfrac{{13}}{{12}}.x$ will do $26m$ length of wall.
 So we can write, $\dfrac{{13}}{{12}}.x$ $ = 26$
Now by cross-multiplication we get-
$13x = 12 \times 26$
Now we get the value of $x$,
So we need to divide $\dfrac{{12 \times 26}}{{13}}$
Therefore we get $x = \dfrac{{12 \times 26}}{{13}} = 24$
Thus, the required number of men is \[24\]

Note: Unitary method is the easiest way of solving this type of arithmetic question where you can get the value of unit work by dividing total work by total number of people.
After getting the unit value you have to multiply it with the required number of people or any other thing to get the final solution.