1. According to the question, initially the value of d is 1 and the value of y is 100. Now we have to find the smallest integer possible for x that will have the value of d as 2.
Now,
firstly imagine value of x as half of y,
x=50. As we put it in the process we will get d as 2 and that sums up that x=50 is possible, so we will have to try a smaller value. Lets take
40. After applying it in the process we can see that d does not equal to 2, hence we take 45 as x. It does fulfill conditions of the question.
To check for a lower value put 44 in the process and we can see that it does not fulfill the condition of d as 2.
Hence
45 must be the smallest possible integer value for x when d will be 2.
(note: I have done this question thorugh trial and error method, because I find the other methods to be lengthy.)
2. Here, we have to compare the final values of r, when x is 15 and 55.
When xwill be
15, initial r will be
50. The value of d will be 4 hence we will have to divide the initial r with 2. Hence the final r will be 25.
when x will be
55, initial r will be
20. the value of d will be 2 hence we don't have to divide it with anything and our initial r is our final r.
Question asks about the difference of the r with respect to different r values.
r when x is 15 - r when x is 55 = 25-20 = 5