Select the set in which the numbers are related in the same way as are the numbers of the following sets. (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)
(59, 83, 97)
(63, 87, 101)

The sets (59, 83, 97) and (63, 87, 101).

Logic: (1st + 3rd) $$\div$$ 2 + 5 = 2nd Number

(59, 83, 97) → (59 + 97) ÷ 2 + 5 = 156 ÷ 2 + 5 = 78 + 5 = 83

(63, 87, 101) → (63 + 101) ÷ 2 + 5 = 164 ÷ 2 + 5 = 82 + 5 = 87

From the given options - 

(a) (67, 91, 115) → (67 + 115) ÷ 2 + 5 = 182 ÷ 2 + 5 = 91 + 5 = 96 $$\ne$$ 91
(b) (71, 95, 109) → (71 + 109) ÷ 2 + 5 = 180 ÷ 2 + 5 = 90 + 5 = 95 = 95
(c) (51, 65, 89) → (51 + 89) ÷ 2 + 5 = 140 ÷ 2 + 5 = 70 + 5 = 75 $$\ne$$ 65
(d) (48, 82, 96) → (48 + 96) ÷ 2 + 5 = 144 ÷ 2 + 5 = 72 + 5 = 77 $$\ne$$ 82

Correct answer is (b).