A contractor undertakes to make a tunnel in $40$ days and employs $25$ men. After $24$ days, he finds that only one-third of the road is made. How many extra men should he employ so that he is able to complete the work $4$ days earlier?

Let's use the work equivalence formula:
$$\frac{M_1\times D_1}{W_1}=\frac{M_2\times D_2}{W_2}$$

Given parameters for the first part of the work:

* $M_1=25\text{ men}$
* $D_1=24\text{ days}$
* $W_1=\frac{1}{3}\text{ of the work}$

Parameters for the remaining part of the work:

* Remaining work: $W_2=1-\frac{1}{3}=\frac{2}{3}$
* Total time scheduled initially was $40$ days. Since the contractor wants to finish the work $4$ days earlier, the total target time becomes $40-4=36$ days.
* Time already spent: $24$ days.
* Remaining days available: $D_2=36-24=12$ days.
* Let total men working in the second phase be $M_2$.

Substituting these values into the formula:

$$\frac{25\times 24}{\frac{1}{3}}=\frac{M_2\times 12}{\frac{2}{3}}$$

Canceling out the denominators:

$$25\times 24=\frac{M_2\times 12}{2}$$

$$25\times 24=M_2\times 6$$

$$M_2=\frac{25\times 24}{6}=25\times 4=100\text{ men}$$

Therefore, the total number of men required is $100$.
The number of extra men to employ is:

$$\text{Extra Men}=M_2-M_1=100-25=75\text{ men}$$