Question

If $20$ men can build a wall $112$ meters long in $6$ days, what length of a similar wall can be built by $25$ men in $3$ days?

Answer 1

Method 1: The problem involves set of $3$ variables, namely - Number of men, Number of days and length of the wall.

Number of Men	Number of days	Length of the wall in metres
$20$	$6$	$112$
$25$	$3$	$x$

Step 1 : Consider the number of men and the length of the wall. As the number of men increases from $20$ to $25$, the length of the wall also increases. So it is in Direct Variation.
Therefore, the proportion is $20:25::112:x$ .....(1)
Step 2: Consider the number of days and the length of the wall. As the number of days decreases from $6$ to $3$, the length of the wall also decreases. So, it is in Direct Variation.
Therefore, the proportion is $6:3::112:x$ ......(2)
Combining (1) and (2), we can write
$\begin{array}{c}20:25\\ 6:3\end{array}::112:x$
We know, Product of Extremes $=$ Product of Means.
$\begin{array}{ccccc}Extremes& & Means& & Extremes\\ 20& :& 25::112& :& x\\ 6& :& 3& & \end{array}$
So, $20\times 6\times x=25\times 3\times 112$
$x=\frac{25\times 3\times 112}{20\times 6}=70$ meters.
Method 2

Number of Men	Number of days	Length of the wall in metres
$20$	$6$	$112$
$25$	$3$	$x$

Step 1: Consider the number of men and length of the wall. As the number of men increases from $20$ to $25$, the length of the wall also increases. It is in direct variation.
The multiplying factor $=\frac{25}{20}$
Step 2: Consider the number of days and the length of the wall. As the number of days decreases from $6$ to $3$, the length of the wall also decreases. It is in direct variation.
The multiplying factor $=\frac{3}{6}$.
$\therefore$ $x=\frac{25}{20}\times \frac{3}{6}\times 112=70$ meters