Question

A boat sails 27 kms down stream in 3 hours but takes 9 hours to sail back the same distance up stream. Calculate the ratio of speed of boat to speed of stream.

• A. 2:1
• B. 3:2
• C. 4:1
• D. 3:4

Hint:

For boats and streams: \[ \text{Downstream Speed}=u+v,\qquad \text{Upstream Speed}=u-v \] where \(u\) is boat speed in still water and \(v\) is stream speed.

Answer 1

The Correct Option is A

Step 1: Calculate downstream and upstream speeds.
Distance travelled in each case = 27 km. Downstream speed: \[ \frac{27}{3}=9 \text{ km/hr} \] Upstream speed: \[ \frac{27}{9}=3 \text{ km/hr} \]

Step 2: Find the speed of the boat and stream.
Let the speed of the boat in still water be \(u\) km/hr and speed of the stream be \(v\) km/hr. \[ u+v=9 \] \[ u-v=3 \] Adding the two equations: \[ 2u=12 \] \[ u=6 \text{ km/hr} \] Subtracting the second equation from the first: \[ 2v=6 \] \[ v=3 \text{ km/hr} \]

Step 3: Find the required ratio.
\[ u:v=6:3=2:1 \] {2:1}