Question

A boat moving upstream takes 8 hours 48 minutes to cover a distance while it takes 4 hours to return to the starting point, downstream. What is the ratio of the speed of boat in still water to that of water current?

• A. 3 : 2
• B. 4 : 3
• C. 8 : 3
• D. 2 : 1

Answer 1

Answer:

C. 8 : 3

Let the Speed of the Boat and Speed of the current be S(bt) and S(ct)

 

Let the distance be 44 KM ( we assume this (because we do not have any distance given, we take LCM of the time taken by boat going upstream and downstream i.e. $\frac{44}{5}hrs$ and 4 hrs )

 

Now speed = Distance/ time taken,

As we have assumed the distance as 44 km so,

 

Upstream speed (U(s))= $\frac{44}{4}$ =11 km/hr and 

 

Downstream speed (D(s)) = $\frac{44}{(\frac{44}{5})}$=5  km/hr

 

We know,

 

Speed of boat - speed of current =Upstream speed(U(s))   and

 

Speed of boat + speed of current= Downstream speed (D(s))

 

So,

S(b)+S(c)= 11 —- eq(1)

S(b)-S(c)= 5 —-- eq(2) 

When both eq. 1&2  are added we get 2S(b)=16

 

 which makes S(bt)=8 km/hr  and S(ct)= 3 km/hr

 

∴  So the ratio of the boat's speed and the current's speed is 8:3.

 

Alternate solution: 

 

We know that Speed of boat = ½ (Downstream speed + Upstream speed),

 

And as we have assumed the distance as 44 km so, we have

 

Upstream speed (U(s))= $\frac{44}{4}$ =11 km/hr and 

 

Downstream speed (D(s)) = $\frac{44}{(\frac{44}{5})}$=5  km/hr

 

So Speed of boat = ½ ( 11+5) =8 km/hr

Speed of current = Speed of boat - Downstream speed

Speed of current = 8- 5= 3 km/hr

∴ The ratio of speed of boat and speed of current is 8:3