Let the three-digit number be XYZ.

This number is such that (100X + 10Y + Z) / (X + Y + Z) is the least possible.

For 100, this ratio is 100/1 = 100 For 101, this ratio is 101/2 = 50.5 For 109, this ratio is 109/10 = 10.9 For 110, this ratio is 110/2 = 55

For 119, this ratio is 119/11 = 10.81 For 129, this ratio is 129/12 = 10.75

So, we can see that in 100-199 range, this ratio will be the least for 199, which is 199/19 = 10.47 Similarly, in 200-299 range, this ratio will be the least for 299, which is 299/20 = 14.95 Similarly, in 300-399 range, this ratio will be the least for 399, which is 399/21 = 19

We can see this ratio is slowly increasing. For 999, it would be 999/27 = 37 So, this ratio is the least for 199.

The difference between the digit at the hundred’s place and the digit at the unit’s place = 9 – 1 = 8 Hence, option (c) is correct.