Explanation:

Correct option 4: 640 km

Given:

• Upstream time to travel from A to B = 12 hours 48 minutes = 12+(48/60)=12.8 hours
• Downstream time to cover 3/4 of the distance = 6 hours
• Speed of current = 15 km/h
• Boat covers the same distance upstream (A to B) and downstream (B to A)

Let the distance between A and B be D km, and let the speed of the boat in still water be B km/h.

Upstream speed = (B – 15) km/h

Time taken to cover D km upstream = D/ (B- 15)  = 12.8 -----------------(1)

Downstream speed = (B + 15) km/h

Time taken to cover (3/4)D downstream = 3D / 4x(B+15) = 6 -----------(2)

Now, 

Solve equation (2)

Substitute Eq (3) into Eq (1)

------------(3)

Multiply both sides by (B-15)

8(B+15)= 12.8(B-15)

Solving for B gives B= 65.

Now substitute B in Eq (3)

D= 8(B +15) = 8(65+15)=8×80=640 km