Question

If downstream speed of a boat is equal to cube of the upstream speed, what will be the maximum value of ratio of speed of boat to speed of stream such that speed of boat and stream are natural number and not equal.

1. 3 : 1 
2. 2 : 1
3. 2 : 3 
4. 5 : 3 
5. 4 : 3 

Answer 1

Correct Answer - Option 4 : 5 : 3 

Given that

Downstream Speed of boat = cube of the upstream speed

Formula Used 

Speed of boat = ( downstream speed + upstream speed )/ 2

Speed of river = (downstream speed – upstream speed )/2

Calculation

Let Upstream speed = x

Downstream speed = x³

Speed of boat = (x³ + x)/2

Speed of river = (x³ – x)/2

Ratio of the speed of the boat and river = (x³ + x)/(x³ – x)

⇒ (x² + 1)/(x² – 1)

Maximum possible for x = 2

Ratio of the speed of the boat and river = (4 + 1)/(4 – 1) = 5/3

∴ Ratio of speed of the boat and  river is 5 ∶ 3