It takes 5 days for a steamboat to travel from A to B along a river. It takes 7 days to return from B to A. How many days will it take for a raft to drift from A to B (assuming all speeds are constant)?

Correct option is B

Given:

• Steamboat takes 5 days from A to B (downstream).
• Steamboat takes 7 days from B to A (upstream).
• Let the distance between A and B = D
• Let the speed of boat in still water = B km/day
• Let the speed of stream = R km/day
• Let the raft's speed = R km/day (since it drifts with stream)

Formula Used:

​Time = Distance / Speed

Solution:

​Let speed downstream = B + R, and speed upstream = B - R
Then:

Using the formula:

• Distance = (B + R) × 5 → [Downstream]
• Distance = (B − R) × 7 → [Upstream]

Since distance is the same both ways:

Step 1:
(B + R) × 5 = (B − R) × 7

Step 2: Expand both sides
5B + 5R = 7B − 7R

Step 3: Rearranging terms
5B + 5R − 7B + 7R = 0
=>−2B + 12R = 0
=> B = 6R

Step 4: Substitute B in downstream equation
Downstream speed = B + R = 6R + R = 7R
Distance = 7R × 5 = 35R

Raft speed = R, so time = distance/speed = 35R / R = 35 days

Final Answer: (B) 35 days