Correct Answer: 8 : 228

Solution : Given:
7 : 198

Find the square of the first number and then multiply by 2 then add 100 to the resultant number to obtain the second number in the given set of numbers –
7 : 198→((7) ² × 2) + 100 = (49 × 2) + 100 = 98 + 100 = 198

Let's check the options –
First option: 9 : 162→((9) ² × 2) + 100 = (81 × 2) + 100 = 162 + 100 = 262 ≠ 162
Second option: 5 : 240→((5) ² × 2) + 100 = (25 × 2) + 100 = 50 + 100 = 150 ≠ 240
Third option: 6 : 72→((6) ² × 2) + 100 = (36 × 2) + 100 = 72 + 100 = 172 ≠ 72
Fourth option: 8 : 228→((8) ² × 2) + 100 = (64 × 2) + 100 = 128 + 100 = 228

So, only the fourth option follows the same pattern as followed by the given set of numbers. Hence, the fourth option is correct.