Question

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 $50 : 45 : 40$ .

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

Accepted Answer

C. Let $D$ be length of the race. $$\frac{S_A}{S_B} = \frac{D}{D-30}, \quad \frac{S_B}{S_C} = \frac{D}{D-20}, \quad \frac{S_A}{S_C} = \frac{D}{D-48}$$ Multiply the first two ratios: $$\frac{D}{D-30} 	imes \frac{D}{D-20} = \frac{D}{D-48} \implies D(D-48) = (D-30)(D-20)$$ $$D^2 - 48D = D^2 - 50D + 600 \implies 2D = 600 \implies D = 300	ext{ m}$$ Statement I is TRUE. Ratio of speeds: $$S_A : S_B : S_C = 300 : 270 : 252 = 50 : 45 : 42$$ Statement II states ratio is $50 : 45 : 40$, which is FALSE.

Statements on Race Distance and Speeds

Explanation

Practise this under exam conditions