At 1.00 pm, Jack walked to school that was between 2.5 km to 3 km from his home, and then returned home (total of 5-6 km) between 55 minutes and 1 hour 5 minutes (65 minutes)

At 1.00 pm. Jill walked 5 km more than Jack and returned home at 3 pm. i.e. 10 to 11 km in 2 hours (120 minutes).

(i) The walking speed of Jill was greater than that of Jack if jack walked for 5 km in 1 hour and JIll walked for 10 km in 2 hours. Then walking speed are equal if Jack walked for 6 km in 1 hour and Jill walked for 11km in 2 hours, then the walking speed of Jack is greater. Therefore, this statement is wrong.

(ii) Jack's walking speed was close to 3 km per hour. Jack cover a distance of 5-6 km in 55 minutes - 65 minutes.
$$His\ walking\ speed\ =\ \left(5\ to\ 6\ \right)\frac{km}{1.08\ hr}\ =\ 5.5\ \frac{km}{hr}$$
Thus, this is greater than 3km/hr. This statement is also wrong.

(iii) Had Jack covered 0.5 more kilometres every 30 minutes, his walking speed would have been greater than Jill's. If Jack covered 0.5 km more every 30 minutes, he will cover 1 more km every 1 hour, and he will walk 6-7 km in between 55-65 minutes.

Jill walked about 10-11 km in 2 hours or walked about 5.5 km in 1 hour.

Therefore, without adding 1 more km every hour, Jack's walking speed is greater than that of Jill. Hence after adding 1 more km every hour, Jack's walking speed will definitely be greater than that of Jill. This statement is CORRECT..

Final answer is OPTION C