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CAT 2020 Quant Question [Slot 2] with Solution 03

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

1. 500
2. 475
3. 550
4. 450
Option: 4
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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