Three persons $$A,B,C$$ participate in a running race of $$1\text{ km}$$ distance. When $$A$$ and $$B$$ run, $$A$$ wins by $$60$$ seconds. When $$A$$ and $$C$$ run, $$A$$ wins by $$375\text{ m}$$. When $$B$$ and $$C$$ run, $$B$$ wins by $$30$$ seconds. If the time taken by $$B$$ to run $$1\text{ km}$$ is $$x$$ minutes and $$30$$ seconds, then $$x$$ is
Correct Answer: 3
Solution
Let the times taken by $$A,B,C$$ be $$T_A,T_B,T_C$$ seconds. Then $$T_B=T_A+60$$ and $$T_C=T_B+30=T_A+90$$. Since $$C$$ covers only $$625\text{ m}$$ when $$A$$ covers $$1000\text{ m}$$, $$T_C=\frac{8}{5}T_A$$. Hence $$T_A+90=\frac{8}{5}T_A$$, giving $$T_A=150$$ and $$T_B=210$$ seconds, which is $$3$$ minutes $$30$$ seconds.
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