To solve this problem, let's assume the current age of the ship as 'S' and the current age of the ship's boiler as 'B'.
According to the given information, the ship is currently twice as old as the ship's boiler was when the ship was as old as the boiler is.
So, when the ship was as old as the boiler is, the age of the ship was 'B' and the age of the boiler was 'B'.
Therefore, we can write the equation:
S = 2(B - S)
Solving this equation will give us the ratio of the boiler's age to the ship's age.
Expanding the equation, we get:
S = 2B - 2S
Adding '2S' to both sides:
S + 2S = 2B
Combining like terms:
3S = 2B
Dividing both sides by 'B':
(3S) / (2B) = 1
Simplifying the expression, we get:
(3/2)(S/B) = 1
Therefore, the ratio of the boiler's age to the ship's age is 3/2, which is equivalent to 3/4.
Hence, the correct answer is D) 3/4.