Let us assume that the speed of A is x and that of B is y.

Then, according to the given information, x = 1.5y.

The time taken by A and B to cover a distance of d meters will be given by:

Time taken by A = d/x
Time taken by B = d/y

Now, since A and B have to reach the winning post at the same time, we have:

d/x = d/y

On solving, we get:

x = y

Substituting the value of x in the equation x = 1.5y, we get:

1.5y = y
y = 0

This is not possible as the speed of B cannot be zero.

Therefore, the given statement is not possible.

Now, let us assume that A has a start of 50 m.

Then, the total distance of the race will be given by:

Total distance = Distance covered by A + Distance covered by B + 50 m

Let us assume that this total distance is d.

Then, the time taken by A and B to cover this distance will be given by:

Time taken by A = (d - 50)/x
Time taken by B = d/y

Now, since A and B have to reach the winning post at the same time, we have:

(d - 50)/x = d/y

On solving, we get:

d = 150 m

Therefore, the winning post should be 150 m away in order for A and B to reach at the same time.

Hence, the correct answer is Option D 150 m.

If you think the solution is wrong then please provide your own solution below in the comments section .