The speeds of four cars are 2u 3u 4u and xu and the time taken by them to cover the same distance is...........

Quantitative Aptitude (CDS) Time & distance

The speeds of four cars are 2u, 3u, 4u and xu and the time taken by them to cover the same distance is xt, 4t, 3t and 2t respectively, where.

x, u, t are real numbers. What is the value of x?

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2024 CDS -1 MATH

- Consider the relationship between speed, time, and distance: Distance = Speed × Time.

- For each car, since they all cover the same distance, you can set up equations:

1. Car 1: \( \text{Distance} = 2u \times xt \)

2. Car 2: \( \text{Distance} = 3u \times 4t \)

3. Car 3: \( \text{Distance} = 4u \times 3t \)

4. Car 4: \( \text{Distance} = xu \times 2t \)

- Equating equations 1 and 2: \( 2u \times xt = 3u \times 4t \), simplify to get \( 2x = 12 \), so \( x = 6 \).

- Equating equations 2 and 3: Check consistency and you'll get the same \( x \).

- Equating equations 3 and 4: Continue verifying, \( x = 6 \) holds.

- Option 2: 6 is the correct answer.

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