CAT 2020 Slot 2 QA Question 13: 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

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

Accepted Answer

Let the race distance be $D$ km.

When A finishes, B has covered $D - 45$ km. Hence
$\dfrac{A}{B} = \dfrac{D}{D - 45}$
When B finishes, C has covered $D - 50$ km. Hence
$\dfrac{B}{C} = \dfrac{D}{D - 50}$
When A finishes, C has covered $D - 90$ km. Hence
$\dfrac{A}{C} = \dfrac{D}{D - 90}$

Now
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