The ratio of speeds, of a Bus and Car is 6 : 7. If car covers 364 Km distance in 4 hours, what is the speed of Bus ?

Question

Accepted Answer

To determine the speed of the Bus, we need to use the given ratio of speeds between the Bus and the Car, which is 6:7. We also know that the Car covers 364 km in 4 hours. Let's break down the solution step by step:

1. **Calculate the Speed of the Car:**
   - The Car covers 364 km in 4 hours.
   - Speed of the Car = Distance / Time = 364 km / 4 hours = 91 km/h.

2. **Use the Ratio to Find the Speed of the Bus:**
   - The ratio of the speeds of the Bus to the Car is 6:7.
   - Let the speed of the Bus be 6x and the speed of the Car be 7x.
   - We know the speed of the Car is 91 km/h, so 7x = 91 km/h.
   - Solving for x gives us x = 91 km/h / 7 = 13 km/h.

3. **Calculate the Speed of the Bus:**
   - The speed of the Bus is 6x.
   - Substitute the value of x: Speed of the Bus = 6 * 13 km/h = 78 km/h.

Therefore, the speed of the Bus is 78 km/h, which corresponds to Option 3.

**Explanation of Why Other Options are Incorrect:**

- **Option 1 (60 Km/h):** 
  - If the speed of the Bus were 60 km/h, the ratio of speeds would not be 6:7 when the Car's speed is 91 km/h. The ratio would be 60:91, which simplifies to approximately 6.59:10. This does not match the given ratio of 6:7.

- **Option 2 (72 Km/h):**
  - If the speed of the Bus were 72 km/h, the ratio of speeds would be 72:91, which simplifies to approximately 7.91:10. This does not match the given ratio of 6:7.

- **Option 4 (84 Km/h):**
  - If the speed of the Bus were 84 km/h, the ratio of speeds would be 84:91, which simplifies to approximately 9.23:10. This does not match the given ratio of 6:7.

In conclusion, the only option that satisfies the given ratio of 6:7 with the Car's speed of 91 km/h is Option 3, where the Bus's speed is 78 km/h.