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Statements on Race Distance and Speeds

CMAT 2025 · Quantitative Techniques & Data Interpretation · Medium · Quantitative Aptitude

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In a race A, B and C take part. A beats B by 30 meters, B beats C by 20 meters and A beats C by 48 meters. Given below are two statements: Statement I: The length of the race is 300 meters. Statement II: The speed of A, B and C are in the ratio 50:45:4050 : 45 : 40.

In the light of the above statements, choose the correct answer from the options given below:

  1. A.

    Both Statement I and Statement II are true

  2. B.

    Both Statement I and Statement II are false

  3. C.

    Statement I is true but Statement II is false

  4. D.

    Statement I is false but Statement II is true

Answer

C

Explanation

Let DD be length of the race. SASB=DD−30,SBSC=DD−20,SASC=DD−48\frac{S_A}{S_B} = \frac{D}{D-30}, \quad \frac{S_B}{S_C} = \frac{D}{D-20}, \quad \frac{S_A}{S_C} = \frac{D}{D-48}

Multiply the first two ratios: DD−30×DD−20=DD−48  ⟹  D(D−48)=(D−30)(D−20)\frac{D}{D-30} \times \frac{D}{D-20} = \frac{D}{D-48} \implies D(D-48) = (D-30)(D-20) D2−48D=D2−50D+600  ⟹  2D=600  ⟹  D=300 mD^2 - 48D = D^2 - 50D + 600 \implies 2D = 600 \implies D = 300\text{ m} Statement I is TRUE.

Ratio of speeds: SA:SB:SC=300:270:252=50:45:42S_A : S_B : S_C = 300 : 270 : 252 = 50 : 45 : 42 Statement II states ratio is 50:45:4050 : 45 : 40, which is FALSE.

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