A dog chases rabbit. The rabbit is 125 leaps ahead of itself jumps from dog. The rabbit can jump 4 times in time in which the dog can jump 3 times. The distance covered by the rabbit & dog in one jump is 1.75 and 2.75 m. How many jumps the dog will catch the rabbit ?

Options

A. 175
B. 525
C. 425
D. 575

Answer

To solve the problem of how many jumps the dog will take to catch the rabbit, we can break it down step by step.

### Step-by-Step Solution:

1. **Identify the lead of the rabbit**:
The rabbit is 125 leaps ahead of the dog.

2. **Determine the distance covered in one leap**:
- The distance covered by the rabbit in one jump is 1.75 meters.
- The distance covered by the dog in one jump is 2.75 meters.

3. **Calculate the total distance the rabbit is ahead in meters**:
Since the rabbit is 125 leaps ahead, we calculate the distance in meters:
\[ \text{Distance ahead} = 125 \text{ leaps} \times 1.75 \text{ m/leap} = 218.75 \text{ meters} \]

4. **Calculate the effective distance covered by both the rabbit and the dog in a given time**:
- In the time the dog makes 3 jumps, the rabbit makes 4 jumps.
- Distance covered by the rabbit in 4 jumps:
\[ \text{Distance by rabbit} = 4 \text{ jumps} \times 1.75 \text{ m/jump} = 7 \text{ meters} \]
- Distance covered by the dog in 3 jumps:
\[ \text{Distance by dog} = 3 \text{ jumps} \times 2.75 \text{ m/jump} = 8.25 \text{ meters} \]

5. **Calculate the relative distance covered by the dog compared to the rabbit**:
The dog gains on the rabbit by:
\[ \text{Gain per cycle} = \text{Distance by dog} - \text{Distance by rabbit} = 8.25 \text{ m} - 7 \text{ m} = 1.25 \text{ meters} \]

6. **Determine how many cycles (sets of jumps) it will take for the dog to catch up**:
To find out how many cycles it will take for the dog to cover the initial lead of 218.75 meters:
\[ \text{Number of cycles} = \frac{\text{Distance ahead}}{\text{Gain per cycle}} = \frac{218.75 \text{ m}}{1.25 \text{ m}} = 175 \text{ cycles} \]

7. **Calculate the total number of jumps the dog makes**:
Since each cycle consists of 3 jumps by the dog:
\[ \text{Total jumps by dog} = 175 \text{ cycles} \times 3 \text{ jumps/cycle} = 525 \text{ jumps} \]

### Final Answer:
The dog will catch the rabbit after **525 jumps**.