Question

Speed of a boat in still water is 12 km/hr. The boat goes 24 km along the stream and comes back in 4 hours 30 minutes. What is the speed of the stream?

1. 2 km/h
2. 4 km/h
3. 6 km/h
4. 8 km/h

Answer 1

Correct Answer - Option 2 : 4 km/h

Given:

Speed of a boat in still water = 12 km/h

Distance covered in downstream = 24 km

Time to take the same distance in up stream = 4 hrs 30 minutes

Concept:

Time = Distance/Speed

Upstream speed = (Speed of boat) – (Speed of stream)

Downstream speed = (Speed of boat) + (Speed of stream)

Calculation:

Let, the speed of the stream = x km/hr

Speed of the boat = 12 km/hr

∴ Upstream speed = (12 – x) km/hr

∴ Downstream speed = (12 + x) km/hr

According to the question,

⇒(24/(12 – x)) + (24/(12 + x)) = 4.5 

⇒24 ×(12 + x) + 24 × (12 – x)/ (12 – x) (12 + x) = 9/2

⇒ (288 + 24x + 288 – 24x) × 2 = 9 × (144 – x²)

⇒ 1152 = 9 × (144 – x²)

⇒ 144 – x² = 128

⇒ x² = 16

⇒ x = ±4

∴ Speed of the stream = 4 km/hr