Question

A boat running upstream takes $8$ hours $48$ minutes to cover a certain distance while it takes $4$ hours to cover the same distance running downstream. What is the ratio between the speed of the boat and the speed of the water current respectively?

• A. $2:1$
• B. $3:1$
• C. $8:3$
• D. Cannot be determined

Answer 1

Answer: (C)

$8:3$

We take the speed of the boat = $x$ km/hr and that of the water current = $y$ km/hr.

UPSTREAM : The relative speed = $x-y$ and time = 8 hr. 48min= $\frac{44}{5}$hr.

$\therefore$ The distance = d = $(x-y)\times \frac{44}{5}$............(i).

DOWNSTREAM: The relative speed = x+y and time = 4 hr.

$\therefore$ The distance= d = 4 (x+y)..........(ii).

Comparing (i) & (ii),

$4(x+y)=\frac{44}{5}(x-y)⟹5x+5y=11x-11y⟹3x=8y⟹\frac{x}{y}=\frac{8}{3}$.

So, the required ratio is $8:3$