D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the difference between the digit at the hundred’s place and the digit at the unit’s place of D?

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.