Correct option is B
Given:
A bus starts from point A to B at 50 km/h at 7:00 am.
Another bus starts from point B to A at 60 km/h at 8:00 am.
Both buses meet at 10:00 am.
We are required to find the ratio of the distances AC and BC.
Solution:
Let the distance between A and B be DDD.
The bus from point A to B starts at 7:00 am and travels at 50 km/h. It travels for 3 hours by 10:00 am (since they meet at 10:00 am).
The bus from point B to A starts at 8:00 am and travels at 60 km/h. It travels for 2 hours by 10:00 am.
Distance covered by the bus from A to B:
The distance covered by the first bus is given by:
Distance from A to C=Speed×Time=50 km/h×3 hrs=150 km.\text{Distance from A to C} = \text{Speed} \times \text{Time} = 50 \, \text{km/h} \times 3 \, \text{hrs} = 150 \, \text{km}.Distance from A to C = Speed × Time = 50 km/h × 3hrs = 150km.
So, the bus from A to B covers 150 km by the time it meets the other bus.
Distance covered by the bus from B to A:
The distance covered by the second bus is given by:
Distance from B to C=Speed×Time=60 km/h×2 hrs=120 km.\text{Distance from B to C} = \text{Speed} \times \text{Time} = 60 \, \text{km/h} \times 2 \, \text{hrs} = 120 \, \text{km}.Distance from B to C = Speed × Time = 60km/h × 2hrs = 120km.
So, the bus from B to A covers 120 km by the time it meets the first bus.
Total Distance between A and B:
The total distance between points A and B is the sum of the distances traveled by both buses:
D=150 km+120 km=270 km.D = 150 \, \text{km} + 120 \, \text{km} = 270 \, \text{km}.D = 150 km + 120 km = 270 km.
Ratio of the Distances AC and BC:
Now, we can find the ratio of the distances AC (from A to C) and BC (from B to C):
Final Answer:
The ratio of distances AC to BC is 5:4.
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