Speed of a boat in still water and speed of current is in ratio $6 : 1$. If the difference between distance covered by boat in 2 hours upstream and in 2 hours downstream is 8 km, compare the following quantities:

**Quantity-1:** Speed of boat in still water

**Quantity-2:** Speed of cyclist who goes 28 km in 2 hours

Choose the correct option:

Question

Speed of a boat in still water and speed of current is in ratio $6 : 1$. If the difference between distance covered by boat in 2 hours upstream and in 2 hours downstream is 8 km, compare the following quantities:

**Quantity-1:** Speed of boat in still water

**Quantity-2:** Speed of cyclist who goes 28 km in 2 hours

Choose the correct option:

Accepted Answer

**Solution:**

1. Let the speed of the boat in still water be $6x$ and the speed of the current be $x$ (given ratio $6:1$).

2. Speed upstream = Speed of boat - Speed of current = $6x - x = 5x$

3. Speed downstream = Speed of boat + Speed of current = $6x + x = 7x$

4. Distance covered upstream in 2 hours = $2 	imes 5x = 10x$

5. Distance covered downstream in 2 hours = $2 	imes 7x = 14x$

6. Difference between distances = $14x - 10x = 4x$

Given difference = 8 km

So, $4x = 8 \implies x = 2$

7. Speed of boat in still water = $6x = 6 	imes 2 = 12 	ext{ km/h}$

8. Speed of cyclist = $\frac{28 	ext{ km}}{2 	ext{ hours}} = 14 	ext{ km/h}$

9. Compare Quantity-1 and Quantity-2:

- Quantity-1 = 12 km/h

- Quantity-2 = 14 km/h

Clearly, $12 < 14$

**Answer:** Quantity-1 < Quantity-2 (Option (c))

**Note:** The correct answer option is (c), but since the user input options have (a) as Quantity-1 > Quantity-2 marked, the correct choice is (c). Please verify carefully.

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