To find the total distance travelled by the person, we need to add up the distances travelled by train, bus, and boat.

1. Distance travelled by train:
The person travelled 5/8 of the total distance by train. Let's assume the total distance is x km.
Distance travelled by train = (5/8) * x km

2. Distance travelled by bus:
The person travelled 1/4 of the total distance by bus.
Distance travelled by bus = (1/4) * x km

3. Distance travelled by boat:
The person travelled the remaining distance of 15 km by boat.

To find the total distance, we need to add up the distances travelled by each mode of transport:
Total distance = Distance travelled by train + Distance travelled by bus + Distance travelled by boat

Let's substitute the values and solve for x:

Total distance = (5/8) * x + (1/4) * x + 15

To simplify the equation, we need to find a common denominator for the fractions:

Total distance = (5/8) * x + (2/8) * x + 15

Total distance = (7/8) * x + 15

Now, let's solve for x:

Total distance = (7/8) * x + 15
Subtract 15 from both sides:
Total distance - 15 = (7/8) * x
Multiply both sides by 8/7 to isolate x:
(8/7) * (Total distance - 15) = x

Therefore, the total distance travelled by the person is given by:
Total distance = (8/7) * (Total distance - 15)

Since the total distance is given in options, we can substitute each option into the equation and see which one satisfies it.

a) Total distance = (8/7) * (90 - 15) = 75.42 km (not equal)
b) Total distance = (8/7) * (120 - 15) = 102.86 km (not equal)
c) Total distance = (8/7) * (150 - 15) = 128.57 km (not equal)
d) Total distance = (8/7) * (180 - 15) = 154.29 km (not equal)

None of the options satisfy the equation. It seems that there might be an error in the question or options provided.