Question

Directions: In the following question, two statements are numbered as Quantity I and Quantity II. On solving these statements, we get quantities I and II respectively. Solve both quantities and choose the correct option.

The speed of a motorbike in upstream is 50% less than that of downstream. 

Quantity I: The speed of the stream is how much percentage of the speed of the motorbike downstream? 

Quantity II: The speed of the stream is how much percent less than the speed of the motorbike in still water?

1. Quantity 1 > Quantity 2
2. Quantity 1 ≥ Quantity 2
3. Quantity 1 < Quantity 2
4. Quantity 1 ≤ Quantity 2
5. Quantity 1 = Quantity 2

Answer 1

Correct Answer - Option 3 : Quantity 1 < Quantity 2

Given:

u/s speed = 0.5 × d/s speed

Formula used:

Let the speed of the motorbike in still water = u km per hour and the speed of the stream = v km per hour

the speed of the motorbike in downstream = (u + v) km per hour

the speed of the motorbike in upstream = (u – v) km per hour

Calculations:

According to the question, (u – v) = (100 – 50)%

⇒ (u + v) = 50% of (u + v)

⇒ 2u – 2v = u + v

⇒ u = 3v

⇒ u : v = 3 : 1

Quantity I:

The speed of the motorbike in downstream = 4x km/hr (∵ 3x + x)

⇒ required % = x × (100 / 4x)

⇒ required % = 25%

Quantity II:

Required % = (3 – 1) × 100 / 3

⇒ required % = 66\(\frac{2}{3}\)%

∴ Quantity I < Quantity II