A boat takes 630 minutes to travel from Point A to B and B to Point A. The distance between Point A and B is 72 km. If the ratio of speed of the boat in still water to the speed of water current is 7:1, what is the speed of the boat downstream? (in kmph)

Options

A. 23
B. 12
C. 24
D. 16

Answer

To solve the problem, we need to find the speed of the boat downstream given the total time taken for the round trip and the ratio of the boat's speed in still water to the speed of the water current.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Total time for the round trip (A to B and B to A) = 630 minutes
- Distance from A to B = 72 km
- Ratio of speed of the boat in still water to the speed of the current = 7:1

2. **Convert Total Time to Hours:**
\[ \text{Total time in hours} = \frac{630 \text{ minutes}}{60} = 10.5 \text{ hours} \]

3. **Let the Speed of the Water Current be \( x \) km/h:**
- Speed of the boat in still water = \( 7x \) km/h
- Speed of the boat downstream = \( 7x + x = 8x \) km/h
- Speed of the boat upstream = \( 7x - x = 6x \) km/h

4. **Calculate the Time Taken for Each Leg of the Journey:**
- Time taken to travel from A to B (downstream):
\[ \text{Time}_{AB} = \frac{\text{Distance}}{\text{Speed}} = \frac{72}{8x} \text{ hours} \]
- Time taken to travel from B to A (upstream):
\[ \text{Time}_{BA} = \frac{72}{6x} \text{ hours} \]

5. **Set Up the Equation for Total Time:**
\[ \text{Total time} = \text{Time}_{AB} + \text{Time}_{BA} \]
\[ 10.5 = \frac{72}{8x} + \frac{72}{6x} \]

6. **Combine the Fractions:**
- Find a common denominator (which is \( 24x \)):
\[ 10.5 = \frac{72 \cdot 3}{24x} + \frac{72 \cdot 4}{24x} = \frac{216 + 288}{24x} = \frac{504}{24x} \]
\[ 10.5 = \frac{21}{x} \]

7. **Solve for \( x \):**
\[ 10.5x = 21 \implies x = \frac{21}{10.5} = 2 \text{ km/h} \]

8. **Calculate the Speed of the Boat Downstream:**
\[ \text{Speed downstream} = 8x = 8 \cdot 2 = 16 \text{ km/h} \]

### Final Answer:
The speed of the boat downstream is **16 km/h**.