'A' is 3 times as good a workman as 'B' and therefore is able to complete a job in 36 days less than 'B'. In how many days will they finish it working together?

Given, 

A is three times good a workmen as B. 

So, Ratio of Efficiency of A and B are = 3 : 1

The ratio of time taken by A and b is 1 : 3

Let the time taken by A and B 1x and 3x repectively,

According to question, 

3x - 1x = 36

x = 18 

A will finish the total work in 18 days

B will finish the total work in - $$18\times\ 3\ =\ 54\ days$$

The total work be = 54 units ( LCM of 18 and 54)

We know, Efficiency = $$\frac{\left(Total\ work\right)}{time\ taken}$$

$$\therefore\ $$ Efficiency of A = $$\frac{54}{18}=3$$

$$\therefore$$ Efficiency of B = $$\frac{54}{54}=1$$

Time taken to finish the work together = $$\frac{\left(Total\ work\right)}{A's\ efficiency\ +B's\ efficiency}$$

= $$\frac{54}{3+1}=\frac{54}{4}=13\frac{\ 1}{2}\ days$$

Hence, Option D is correct.