Question

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 $2\frac{1}{3}$ 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 mig

Accepted Answer

D. Statement I: $5(t + \frac{10}{60}) = 6(t - \frac{4}{60}) \Rightarrow 5t + \frac{50}{60} = 6t - \frac{24}{60} \Rightarrow t = \frac{74}{60}$ hours. $P = 5 	imes (\frac{74}{60} + \frac{10}{60}) = 5 	imes \frac{84}{60} = 7$ km. (Statement I is false) Statement II: Ratio of speeds $v_A : v_B = \frac{7}{3} : 1 = 7 : 3$. For Babita covering $y$ meters, Amit covers $80 + y$ meters. $\frac{80+y}{7} = \frac{y}{3} \Rightarrow 240 + 3y = 7y \Rightarrow 4y = 240 \Rightarrow y = 60$. Winning distance = $80 + 60 = 140$ meters. (Statement II is true) Hence, Statement I is false but Statement II is true.

Speed, Distance, Time and Races Statements

Explanation

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