Given information:
A is twice as fast as B.
B is thrice as fast as C.
C travelled a distance in 1 hour 54 minutes.

To find:
The time taken by A to cover the same distance.

Solution:
Let's assume the speed of C as x units per hour.
Therefore, the speed of B would be 3x units per hour, and the speed of A would be 6x units per hour.

Converting 1 hour 54 minutes into minutes:
1 hour = 60 minutes
1 hour 54 minutes = 1 × 60 + 54 = 114 minutes

Since speed is equal to distance divided by time, we can calculate the distance traveled by C in 114 minutes using the formula:

Distance = Speed × Time

Substituting the values:
Distance(C) = x × 114

Since B is thrice as fast as C, the distance traveled by B in the same time would be:

Distance(B) = 3x × 114 = 342x

Similarly, since A is twice as fast as B, the distance traveled by A in the same time would be:

Distance(A) = 6x × 114 = 684x

Since the distances traveled by all three runners are the same, we can equate the distances:

x × 114 = 684x

Dividing both sides of the equation by x:
114 = 684

This is not possible, so our initial assumption that the speed of C is x is incorrect.

Let's assume the speed of C as y units per minute.
Therefore, the speed of B would be 3y units per minute, and the speed of A would be 6y units per minute.

Using the same logic as before, we can equate the distances:

y × 114 = 342y
y × 114 = 684y

Dividing both sides of the equation by y:
114 = 342
114 = 684

This is still not possible, so our assumption that the speed of C is y is also incorrect.

Therefore, we need to assume the speed of C as z units per second.
Therefore, the speed of B would be 3z units per second, and the speed of A would be 6z units per second.

Using the same logic as before, we can equate the distances:

z × 114 × 60 = 342z × 60
z × 114 × 60 = 684z × 60

Dividing both sides of the equation by z:
114 × 60 = 342 × 60
114 = 342

This is still not possible, so our assumption that the speed of C is z is also incorrect.

Hence, there is a contradiction in the given information, and we cannot determine the time taken by A to cover the same distance. Therefore, none of the options provided (A, B, C, or D) is correct.

Note: It seems that there might be an error in the question or the answer options provided.