The sum of 4 prime no of two digit is 204.The sum of 1st and last i.e (p1+p4)is same as the sum of second no p2 and third number p3 i.e (p2+p3) Again p3-p2=2 (p2-p1)=2 (p4-p3).The avg no of all four number is not a prime no. one of this prime number is ? a.23 b.89 c.71 d. cant be determined. solution please..

Let the first number be a and the second number be b.
So, third number = 102 - b and fourth number is 102 - a
p3 - p2 = 102 - 2b
p2 - p1 = b - a
p4 - p3 = 102 - a - 102 + b = b - a
So, 102 - 2b = 2b - 2a => 51 + a = 2b => a = 2b - 51
Average = 51
2b - 51, b, 102 - b, 153 - 2b
Only for b = 41, this condition is satisfied
The numbers are 31, 41, 61, 71