The speed of a boat in still water is 40 km/h, and the speed of the current is 1/4th of speed of boat in still water. If the difference in the time taken by the boat to travel Y km upstream and the same distance downstream is 4 hours, find the value of Y.

The correct answer is 300.

Step 1: Identify the given information.
Speed of the boat in still water (u) = 40 km/h.
Speed of the current (v) = 1/4th of the speed of the boat in still water.
Difference in time taken to travel a distance Y km upstream and downstream = 4 hours.

Step 2: Calculate the speed of the current (v).

$v=\frac{1}{4}\times 40=10\text{ km/h}$

Step 3: Calculate the upstream and downstream speeds.
Upstream speed ($S_{\text{upstream}}$) = Speed of boat - Speed of current = 40 - 10 = 30 km/h.
Downstream speed ($S_{\text{downstream}}$) = Speed of boat + Speed of current = 40 + 10 = 50 km/h.

Step 4: Express the time taken for upstream and downstream journeys.
Time taken to travel distance Y upstream ($T_{\text{upstream}}$):

$T_{\text{upstream}}=\frac{Y}{30}$

Time taken to travel distance Y downstream ($T_{\text{downstream}}$):

$T_{\text{downstream}}=\frac{Y}{50}$

Step 5: Set up the equation based on the given time difference.
Since upstream speed is slower, the time taken upstream is greater than the time taken downstream.

$T_{\text{upstream}}-T_{\text{downstream}}=4$

$\frac{Y}{30}-\frac{Y}{50}=4$

Step 6: Solve for Y.
Find a common denominator for 30 and 50, which is 150.

$\frac{5Y-3Y}{150}=4$

$\frac{2Y}{150}=4$

$2Y=4\times 150$

$2Y=600$

$Y=\frac{600}{2}=300$

Thus, the value of Y is 300 km.