Question

Shyam ran in a race in his club. If one more runner had finished before him there would have been as many people in front of him as behind him. But if there had been one more runner finishing behind him there would have been three times as many behind him as in front of him. How many people took part in the race and at what position did Shyam finish?

Answer 1

Let $x$ persons finished in front of Shyam and $y$ persons finished behind him.

If one more person finished ahead of him, there would have been one person less behind him.

According to the first condition, $x+1=y-1$
$\Rightarrow y=x+2$ .....(i)
According to the second condition, $y+1=3(x-1)$
$\Rightarrow y=3x-4$ ....(ii)
Equating (i) and (ii), we get

$x+2=3x-4$
$\Rightarrow x=3$ and $y=5$.
Therefore, there were $3$ persons ahead of Shyam and $5$ persons behind him.

Hence, $9$ persons took part in the race and Shyam finished $4th$.