Mark's walking speed = 5km/h
Steve's walking speed = 10km/h
Mark walked for 1 hour, turned around and walked back to his starting point (another 1 hour).
Mark rested for half an hour at the starting point.
Total time = 1 + 1 + 1 0.5 = 2.5 hours
Distance covered by Mark in this 2.5 hours = 5 * 2.5 = 12.5km
Distance covered by Steve in this 2.5 hours = 10 * 2.5 = 25km
The speed of taxi hired by Mark = 30km/hr
Charges for the first 2km = $10
Charges for every 500m = $2
Let the total distance covered by Steve in t hours = x km
i.e t = x/10
The total distance covered by taxi to catch up with Steve = distance covered by Steve in 2.5 hours + distance covered by Steve in t hours = (25 + x) km

Time taken by Taxi to cover (25 + x)km in t hours =>
$$=\frac{25+x}{30}$$
Equating the time taken by Steve and Taxi =>
$$\frac{x}{10}=\frac{25+x}{30}$$
$$30x=250+10x$$
$$30x-10x=250$$
$$20x=250$$
$$x=\frac{250}{20}=12.5km$$
Therefore, the total distance travelled by the taxi = 25 + 12.5 = 37.5km
Charges for the first 2km covered = $10
For the remaining (37.5 - 2 = 35.5km)=?
$2 per 500m or $4 per 1000m/1km
=>35.5 * 4 = $142
Total charges = $10 + $142 = $152
Answer = option D