Question

The figure shows three paths connecting points $a$ and $b$. A single force $F$ does the indicated work on a particle moving along each path in the indicated direction. On the basis of this information, is force $F$ conservative?

Answer 1

No based on this information force $F$ is not conservative.

On one path work done by force from $a$ to $b$ is $60J$.

and on another path work done by force from $b$ to $a$ is $60J$.

$b$ to $a$ is the opposite vectors of $a$ to $b$ if $F$ were too be conservative they should be same.