Two ships are approaching a port along straight routes at constant speeds. Initially, the two ships and the port formed an equilateral triangle with sides of length 24 km. When the slower ship travelled 8 km, the triangle formed by the new positions of the two ships and the port became right-angled. When the faster ship reaches the port, the distance, in km, between the other ship and the port will be

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#### Step 1: Key Observations  
- The initial positions of the two ships and the port form an equilateral triangle with sides of 24 km.

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1743586116/aptidude_questions/vf5jodmjcedvnmkspfdv.png)

- After traveling, the positions of the two ships and the port form a right-angled triangle.

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1743586122/aptidude_questions/uvpo3pfiwhcgmbdb1azm.png)

- The slower ship has traveled 8 km to reach its new position.  
- The faster ship travels at twice the speed of the slower ship.

#### Step 2: Analyze Triangle APB  
Let:  
- $$ P $$ = Port, $$ S $$ = Initial position of slower ship, $$ F $$ = Initial position of faster ship.  
- After traveling, let $$ A $$ = New position of slower ship, and $$ B $$ = New position of faster ship.

Since triangle $$ APB $$ is right-angled:  
- Angle $$ APB = 90^\circ $$.  
- Angle $$ PAB = 60^\circ $$ (as it is part of an equilateral triangle).  
- This makes triangle $$ APB $$ a **30°–60°–90° triangle**, where:  
  - $$ BP = \frac{1}{2} 	imes AP $$.

#### Step 3: Calculate Distances in Triangle APB  
From given data:  
- The slower ship has traveled $$ PA = 8 	ext{ km} $$.  
- Thus, in triangle APB:  
  $$
  BP = \frac{1}{2} 	imes AP = \frac{1}{2} 	imes 8 = 4 	ext{ km}.
  $$
- The distance covered by the faster ship is:  
$$
BF = FP - BP = 24 - 4 = 16 	ext{ km}.
$$

#### Step 4: Speed Ratio and Remaining Distance for Slower Ship  
The ratio of speeds of the faster and slower ships is:  
$$
	ext{Speed Ratio} = \frac{	ext{Distance covered by Faster Ship}}{	ext{Distance covered by Slower Ship}} = \frac{16}{8} = 2:1.
$$

When the faster ship reaches the port (covering a total distance of 24 km), the slower ship will have covered half that distance:  
$$
	ext{Distance covered by slower ship} = \frac{24}{2} = 12 	ext{ km}.
$$

The total distance from the port to the slower ship is:  
$$
	ext{Remaining Distance} = Total Distance - Distance Covered = 24 - 12 = 12 	ext{ km}.
$$

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### Final Answer:  
The distance between the slower ship and the port when the faster ship reaches it is **12 km**, and the correct answer is **B**.

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