Question
In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is
- 500
- 475
- 550
- 450
Option: 4
Solution:
Solution:
Let the length of the racetrack be D.
When A covers D km, B covers ( D -45) km and C covers (D-90) km
When B covers D km, C covers ( D -50) km
The ratio of the speeds of the racers is same as the ratio of the distance travelled in a given time period.
Ratio of speed of B and C is \(\frac{{{\text{ Speed of }}B}}{{{\text{ Speed of }}C}} = \frac{{D - 45}}{{D - 90}} = \frac{D}{{D - 50}}\)
\( \Rightarrow \frac{D}{{D - 50}} = \frac{{45}}{{40}}\)
\( \Rightarrow 40D = 45D - 50 \times 45\)
\( \Rightarrow D = 450\)
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