A boat goes 270 km upstream in 54 hours and a distance of 448 km downstream in 64 hours. Find the speed of the boat in still water. (In kmph) 

Given:

A boat goes 270 km upstream in 54 hours and a distance of 448 km downstream in 64 hours.

Formula used:

Let the speed of the boat in still water be b km/h and the speed of the current be c km/h.

Speed upstream = b - c

Speed downstream = b + c

Using the formula: Distance = Speed × Time

Calculations:

For upstream:

270 = (b - c) × 54

⇒ b - c = \(\dfrac{270}{54}\)

⇒ b - c = 5        ..........(1)

For downstream:

448 = (b + c) × 64

⇒ b + c = \(\dfrac{448}{64}\)

⇒ b + c = 7       .............(2)

Adding the two equations:

b - c + b + c = 5 + 7

⇒ b = 6

∴ The correct answer is option (4).