The shaded portion of each of the given figures represents the fraction of the total work completed independently by four workers P, Q, R, and S when they were given the same work. Find who has done the maximum work.

The work done by the workers P, Q, R and S is represented by the given images.  

Circle P is divided into two equal parts, out of which, one part is shaded.

Therefore work done by P= $\frac{1}{2}$. 

Similarly, 

Work done by Q= $\frac{1}{4}$.

 Work done by R= $\frac{3}{4}$.

Work done by S= $\frac{1}{8}$.

Now let's compare the fractions, $\frac{1}{2}$,$\frac{1}{4},\frac{3}{4},\frac{1}{8}$.

LCM = 24.

$\frac{1}{2}$ = $\frac{1}{2}\times \frac{12}{12}=\frac{12}{24}$

$\frac{1}{4}$ = $\frac{1}{4}\times \frac{6}{6}=\frac{6}{24}$

$\frac{3}{4}$ = $\frac{3}{4}\times \frac{6}{6}=\frac{18}{24}$

 $\frac{1}{8}$= $\frac{1}{8}\times \frac{3}{3}=\frac{3}{24}$

Now compare the numerator, 18 > 12 > 6 > 3

$\frac{18}{24}$>$\frac{12}{24}$>$\frac{6}{24}$>$\frac{3}{24}$

Thus, it can be said that $\frac{3}{4}>\frac{1}{2}>\frac{1}{4}>\frac{1}{8}$.

Hence, the maximum work was done by R.