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Speed, Distance, Time and Races Statements

CMAT 2023 · Quantitative Techniques & Data Interpretation · Medium · Speed Time Distance

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Given below are two statements : Statement I : Ravi walks from his house at a speed of 5 km per hour and reaches the college 10 minutes late. If he increases the speed by 1 km per hour next day, he reaches the college 4 minutes earlier than the scheduled time. If the college is P km far from his house, then P = 7.5 km. Statement II: Amit runs 2132\frac{1}{3} times as fast as Babita. If Amit gives Babita a start of 80 meters, then the winning post must be 140 meters far so that Amit and Babita might reach it at the same time. 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

D

Explanation

Statement I: 5(t+1060)=6(t−460)⇒5t+5060=6t−2460⇒t=74605(t + \frac{10}{60}) = 6(t - \frac{4}{60}) \Rightarrow 5t + \frac{50}{60} = 6t - \frac{24}{60} \Rightarrow t = \frac{74}{60} hours. P=5×(7460+1060)=5×8460=7P = 5 \times (\frac{74}{60} + \frac{10}{60}) = 5 \times \frac{84}{60} = 7 km. (Statement I is false)

Statement II: Ratio of speeds vA:vB=73:1=7:3v_A : v_B = \frac{7}{3} : 1 = 7 : 3. For Babita covering yy meters, Amit covers 80+y80 + y meters. 80+y7=y3⇒240+3y=7y⇒4y=240⇒y=60\frac{80+y}{7} = \frac{y}{3} \Rightarrow 240 + 3y = 7y \Rightarrow 4y = 240 \Rightarrow y = 60. Winning distance = 80+60=14080 + 60 = 140 meters. (Statement II is true)

Hence, Statement I is false but Statement II is true.

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