Question:medium

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

Updated On: Jan 15, 2026
  • 500
  • 475
  • 550
  • 450
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The Correct Option is D

Solution and Explanation

Let the length of the racetrack be \( D \).

Given:

  • When A completes distance \( D \), B covers \( D - 45 \), and C covers \( D - 90 \).
  • When B completes distance \( D \), C covers \( D - 50 \).

 Step-by-Step Explanation:

Using the principle that speed is proportional to distance covered in the same time:

From the first condition: \[ \frac{\text{Speed of B}}{\text{Speed of C}} = \frac{D - 45}{D - 90} \]

From the second condition: \[ \frac{\text{Speed of B}}{\text{Speed of C}} = \frac{D}{D - 50} \]

Equating the two ratios: \[ \frac{D - 45}{D - 90} = \frac{D}{D - 50} \]

Cross-multiplication yields: \[ (D - 45)(D - 50) = D(D - 90) \]

Expanding both sides: \[ D^2 - 95D + 2250 = D^2 - 90D \]

Subtracting \( D^2 \) from both sides and rearranging: \[ -95D + 2250 = -90D \Rightarrow -5D = -2250 \Rightarrow D = 450 \]

 Final Answer:

\[ \boxed{D = 450} \]

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