Answer:
a. They both reach at the same time.
Explanation:
On a frictionless incline, the only force that moves the person downwards is the x-component of the persons weight. (x-direction is the direction along the incline.)
[tex]F = mg\sin(\theta)[/tex]
Here, θ is the angle of the incline above horizontal.
This force is equal to 'ma' according to Newton's Second Law.
Comparing the weights of the two persons gives
[tex]F_1 = 85g\sin(\theta) = 85a_1\\F_2 = 75g\sin(\theta) = 75a_1\\a_1 = g\sin(\theta)\\a_2 = g\sin(\theta)[/tex]
Since the accelerations of both persons are the same, they reach the bottom at the same time.
The crucial point here is that the acceleration on a frictionless incline is independent from the mass of the object. If there were friction on the surface, then the person with smaller mass would reach the bottom first.
