Explanation:

Let’s break it down:

- First pair: 8 : 108.

If you look closer, 8 × 8 = 64, and 8 × 8 = 64 + 8 × 8/2 = 64 + 32 = 96.

But that’s not 108.

Try: (8 × 8) + (8 × 5.5) = 64 + 44 = 108.

No, that’s a stretch.

Wait. 8 × 13.5 = 108. Where’s the pattern? Maybe: 8² + 4 × 8 = 64 + 32 = 96. Not matching.

Let’s try 8³ - 8 = 512 - 8 = 504. Still off.

Let’s check 8 × 13.5 = 108, so 13.5 is the multiplier.

Try the same with 12: 12 × 13.5 = 162. But that’s not among the options.

Maybe it’s like this: 8 × (8 + 5.5) = 8 × 13.5 = 108, so 12 × (12 + 5.5) = 12 × 17.5 = 210.

Still not there.

Now, try adding cubes:

8 : 108. 8³ = 512.

8³ - 8² = 512 - 64 = 448.

Not matching.

Next,

How about 8: 8 × (8 + 5.5) = 8 × 13.5 = 108.

Check difference: 108 - 8 = 100, nowhere close.

Try this:

Is 108 = (8 × 8) + (8 × 5.5) ? 64 + 44 = 108.

Yes! That fits!

So, pattern is n × n + n × 5.5 = n × (n + 5.5)

Now for the second pair:

n = 12

12 × (12 + 5.5) = 12 × 17.5 = 210

Check the options:

Option 1: 208

Option 2: 225

Option 3: 135

Option 4: 150

Closest is 208 (very close to 210, maybe a typo/match in exam), but none is 210.

Here’s what each option would look like:

- 12 × (12 + 5.33) ˜ 208 (so, matches pattern if using 5.33 instead of 5.5—but 5.5 was used above, so a small difference)

- 12 × (12 + 6.75) ˜ 225

- 12 × (12 + 1.25) ˜ 135

- 12 × (12 + 0.5) ˜ 150

So, Option 1, 208, is the closest to the pattern because it’s almost matching the multiplier found in the first pair.

Correct answer: Option 1, 208