Two siblings Mark and Steve start from the same point and walk in the

First, let's calculate the distance covered by Steve till the time Mark hires the taxi.

No. of hours after which the taxi is hired = 2.5
Distance covered by Steve (D) = 10 x 2.5 (Speed x Time) = 25 kilometers

Now, to calculate the amount paid by Mark to the taxi driver, we need to know the distance travelled.
The info that is given to us -> Mark only uses the taxi to catch up with Steve.

So the time travelled for both Mark in the taxi and Steve will be the same when Mark catches up with Steve.

D = S x T
T = \(\frac{D}{S}\)

T (Mark in taxi) = T (Steve)

Let distance be x

T (Mark in taxi) = \(\frac{x}{30}\)

T (Steve) = \(\frac{(x-25)}{10}\) -> (As Steve has already covered 25 kilometers)

Equating the two we get:
\(\frac{(x-25)}{10}\) = \(\frac{x}{30}\)

\(20 x = 750\)

\(x = 37.5\)

Distance travelled by Mark in taxi = \(x\) = 37.5 kilometers

Amount paid = 10 + \((x-2)\)*2*2 (Remaining distance multiplied by 2 as the rate after the first 2 kilometers is given per 500 meters)
= 10 + (35.5*4)
= 10 + 142
= $152

Option D