The ratio of speeds of a train and a car is 16 : 15, respectively. A bus covers a distance of 480 km in 8 hours. If the speed of the bus is 3/4th of the speed of the train, then the distance covered by the car in 6 hours is:

450 km

The correct answer is Option (1) → 450 km

Step 1: Find the speed of the bus

Distance = 480 km, Time = 8 hours

$\text{Speed of bus} = \frac{480}{8} = 60 \text{ km/h}$

Step 2: Relate bus speed to train speed

$\text{Speed of bus} = \frac{3}{4} \times \text{Speed of train}$

$60 = \frac{3}{4} \times \text{Speed of train} \Rightarrow \text{Speed of train} = \frac{60 \times 4}{3} = 80 \text{ km/h}$

Step 3: Find speed of car

Given speed ratio of train : car = 16 : 15

$\text{Speed of car} = \frac{15}{16} \times 80 = 75 \text{ km/h}$

Step 4: Distance covered by car in 6 hours

$\text{Distance} = \text{Speed} \times \text{Time} = 75 \times 6 = 450 \text{ km}$