Solution:The pattern followed here is :Numerical position of letter get added and multiply by total number of letter to get the code.
PATNA → P(16) + A(1) + T(20) + N(14) + A(1) ⇒ (16 + 1 + 20 + 14 + 1) = 52
Total number of letters = 5
So, 52 × 5 = 260
GOA = → G(7) + O(15) + A(1) ⇒ (7 + 15 + 1) = 23
Total number of letters = 3
So, 23 × 3 = 69
Similarly,
RANCHI → R(18) + A(1) + N(14) + C(3) + H(8) + I(9) ⇒ (18 + 1 + 14 + 3 + 8 + 9) = 53
Total number of letters = 6
So, 53 × 6 = 318
Hence, 318 is the correct answer.