Ravi moving with constant speed of 20 km/h from his home, reaches school on time. If he moves with 30 km/h, then reaches 18 minutes before school time. Distance of school from his home is :

Question

Accepted Answer

To determine the distance of the school from Ravi's home, we need to analyze the given information and use it to support Option 1 as the correct answer.

1. **Explanation for Option 1 (18 km):**

- Ravi travels at a constant speed of 20 km/h and reaches school on time. Let's denote the time taken to reach school at this speed as $ t $ hours.
   - Therefore, the distance to the school can be expressed as:
     $$
     \text{Distance} = \text{Speed} \times \text{Time} = 20 \times t
     $$
   - When Ravi travels at 30 km/h, he reaches 18 minutes earlier. Converting 18 minutes to hours gives us 0.3 hours.
   - The time taken at 30 km/h is $ t - 0.3 $ hours.
   - The distance to the school can also be expressed as:
     $$
     \text{Distance} = 30 \times (t - 0.3)
     $$
   - Since both expressions represent the same distance, we can set them equal to each other:
     $$
     20t = 30(t - 0.3)
     $$
   - Solving for $ t $:
     $$
     20t = 30t - 9
     $$
     $$
     9 = 10t
     $$
     $$
     t = 0.9 \text{ hours}
     $$
   - Substituting $ t = 0.9 $ back into the distance equation:
     $$
     \text{Distance} = 20 \times 0.9 = 18 \text{ km}
     $$
   - Therefore, the distance of the school from Ravi's home is 18 km, which supports Option 1 as the correct answer.

2. **Explanation for why other options are incorrect:**

- **Option 2 (12 km):** If the distance were 12 km, then at 20 km/h, the time taken would be $ \frac{12}{20} = 0.6 $ hours. At 30 km/h, the time would be $ \frac{12}{30} = 0.4 $ hours. The difference in time is 0.2 hours (12 minutes), not 18 minutes. Therefore, this option is incorrect.
   
   - **Option 3 (16 km):** If the distance were 16 km, then at 20 km/h, the time taken would be $ \frac{16}{20} = 0.8 $ hours. At 30 km/h, the time would be $ \frac{16}{30} \approx 0.533 $ hours. The difference in time is approximately 0.267 hours (16 minutes), not 18 minutes. Therefore, this option is incorrect.
   
   - **Option 4 (24 km):** If the distance were 24 km, then at 20 km/h, the time taken would be $ \frac{24}{20} = 1.2 $ hours. At 30 km/h, the time would be $ \frac{24}{30} = 0.8 $ hours. The difference in time is 0.4 hours (24 minutes), not 18 minutes. Therefore, this option is incorrect.

In conclusion, the calculations and logical reasoning confirm that the distance of the school from Ravi's home is 18 km, making Option 1 the correct answer.