Races And Games — Part 2 MCQs with Explanations

Shyam's speed = $$\frac{{200}}{{20}}$$ = 100 m/sec. Time constant \[\begin{array}{*{20}{c}} {}&{{\text{Ram}}}&{}&{{\text{Shyam}}} \\ {{\text{Distance}} \to }&{1200}&:&{1000} \\ {}&{12}&:&{10} \\ {{\text{Speed}} \to }&{12}&:&{10 = 12} \end{array}\]

\[\begin{array}{*{20}{c}} {\text{A}}&{\text{B}}&{\text{C}} \\ {1000}&{960}&{930} \end{array}\] ⇒ B can give C a start of 30 meters in a 960 meters race $$\eqalign{ & \Rightarrow 960\,{\text{units}} \to 30 \cr & 1\,{\text{unit}} \to \frac{1}{{32}} \cr & 1000\,{\text{units}} \to \frac{{1000}}{{32}} = 31\frac{1}{4}{\text{ meters}} \cr} $$

\[\begin{array}{*{20}{c}} {}&{{\text{Anil}}}&{}&{{\text{Bakul}}} \\ {{\text{Distance}} \to }&{1500}&{}&{1350} \\ {}&{10}&:&9 \\ {}&{{\text{Bakul}}}&{}&{{\text{Charles}}} \\ {{\text{Distance}} \to }&{1500}&{}&{1425} \\ {}&{60}&:&{57} \end{array}\] Anil beats Charles by $$\eqalign{ & = \frac{{87}}{{600}} \times 1500 \cr & = \frac{{435}}{2} \cr & = 217.50{\text{ m}} \cr} $$

100 m is the correct answer to “In a 1000 m race, Arjun, Balaji and Charan are running. Arjun beats Balaji by 100 m, and Balaji beats Charan by 100 m. In the next 1000 m race (the speeds are the same as in the previous), Balaji gives Charan a head start of 100 m, and Arjun gives Balaji a head start of 100 m. Find the distance by which the winner is ahead of the person just behind him.”. This question is standard in competitive examination syllabi for Races And Games.

50 m is the correct answer to “In a race of 800 m, Ram can beat Shyam by 50 m, and in a race of 600 m, Shyam can beat Ghanshyam by 40 m. By how many metres will Ram beat Ghanshyam in a race of 400 m”. This question is standard in competitive examination syllabi for Races And Games.