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Car Race Distance

CAT 2020 Slot 2 · Quantitative Ability · Medium · Arithmetic

This is a medium Quantitative Ability question from the CAT 2020 Slot 2 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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In a car race, car A beats car B by 45 km45\text{ km}, car B beats car C by 50 km50\text{ km}, and car A beats car C by 90 km90\text{ km}. The distance (in km) over which the race has been conducted is

  1. A.

    550

  2. B.

    475

  3. C.

    500

  4. D.

    450

Answer

D

Explanation

Let the total distance of the race be D kmD\text{ km}. When car A finishes D kmD\text{ km}, car B has covered D−45 kmD - 45\text{ km} and car C has covered D−90 kmD - 90\text{ km}. The ratio of speeds of B and C is: VBVC=D−45D−90\frac{V_B}{V_C} = \frac{D - 45}{D - 90} Also, when car B finishes D kmD\text{ km}, car C covers D−50 kmD - 50\text{ km}, so: VBVC=DD−50\frac{V_B}{V_C} = \frac{D}{D - 50} Equating the two ratios: D−45D−90=DD−50\frac{D - 45}{D - 90} = \frac{D}{D - 50} (D−45)(D−50)=D(D−90)(D - 45)(D - 50) = D(D - 90) D2−95D+2250=D2−90DD^2 - 95D + 2250 = D^2 - 90D 5D=2250  ⟹  D=4505D = 2250 \implies D = 450 Hence, the race distance is 450 km450\text{ km}.

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