The average of 4 distinct prime numbers a, b, c, d is 35, where a < b < c < d. a and d are equidistant from 36 and b and c are equidistant from 34 and a, b are equidistant from 30 and c and d are equidistant from 40. The difference between a and d is:

Given, 

The average of the four prime numbers = 35.

a + b + c + d = 35 * 4 = 140.

Since a and d are equidistant from 36.

a + d = 72 --- Eq (1)

b + c = 68 --- Eq (2)

a + b = 60 --- Eq (3) and c + d = 80 --- Eq (4)

Using the equation (3) let us look for the prime values of a and b and the corresponding values of c and d using Eq 2 and 1.

Also given that a < b < c < d.

 (a, b, c, d) = 29, 31, 37, 43

d - a = 43 - 29 = 14

B is the correct answer.